Multiply <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mi>a</mi><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mi>a</mi></msqrt><mo>-</mo><msqrt><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>-</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mi>a</mi><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mi>a</mi></msqrt><mo>-</mo><msqrt><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>-</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac></mstyle></math> .

Expand the denominator using the FOIL method.

Simplify.

Apply the distributive property.

Combine using the product rule for radicals.

Raise <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mo>+</mo><mi>n</mi></mrow></msup></mstyle></math> to combine exponents.

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Rewrite using the commutative property of multiplication.

Simplify each term.

Pull terms out from under the radical.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><msqrt><mi>a</mi><mi>b</mi></msqrt><msqrt><mi>b</mi></msqrt></mstyle></math> .

Combine using the product rule for radicals.

Raise <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mo>+</mo><mi>n</mi></mrow></msup></mstyle></math> to combine exponents.

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Reorder <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> and <math><mstyle displaystyle="true"><msup><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical.

Use <math><mstyle displaystyle="true"><mroot><mrow><msup><mrow><mi>a</mi></mrow><mrow><mi>x</mi></mrow></msup></mrow><mrow><mi>n</mi></mrow></mroot><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msup></mstyle></math> to rewrite <math><mstyle displaystyle="true"><msqrt><mi>b</mi></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mi>b</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Use <math><mstyle displaystyle="true"><mroot><mrow><msup><mrow><mi>a</mi></mrow><mrow><mi>x</mi></mrow></msup></mrow><mrow><mi>n</mi></mrow></mroot><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msup></mstyle></math> to rewrite <math><mstyle displaystyle="true"><msqrt><mi>a</mi></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Factor <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><msup><mrow><mi>b</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> out of <math><mstyle displaystyle="true"><mi>a</mi><msup><mrow><mi>b</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mo>-</mo><mi>b</mi><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Move <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><msup><mrow><mi>b</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> out of <math><mstyle displaystyle="true"><mi>a</mi><msup><mrow><mi>b</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Factor <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><msup><mrow><mi>b</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mi>b</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><msup><mrow><mi>b</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> out of <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><msup><mrow><mi>b</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mo>)</mo></mrow><mo>+</mo><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><msup><mrow><mi>b</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mrow><mo>(</mo><mo>-</mo><msup><mrow><mi>b</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mo>)</mo></mrow></mstyle></math> .

Do you know how to Evaluate ( square root of ab)/( square root of a+ square root of b)? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name | eight hundred eighty-seven million four hundred fifty-six thousand six hundred thirty |
---|

- 887456630 has 16 divisors, whose sum is
**1607599440** - The reverse of 887456630 is
**036654788** - Previous prime number is
**157**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 47
- Digital Root 2

Name | one billion eight hundred sixty million nine hundred ninety-nine thousand four hundred eight |
---|

- 1860999408 has 256 divisors, whose sum is
**14282231040** - The reverse of 1860999408 is
**8049990681** - Previous prime number is
**43**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 54
- Digital Root 9

Name | six hundred eighteen million one hundred twenty-eight thousand six hundred sixty-three |
---|

- 618128663 has 8 divisors, whose sum is
**629352960** - The reverse of 618128663 is
**366821816** - Previous prime number is
**907**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 41
- Digital Root 5