Math / Numbers & Operations

Question $\frac{\sqrt{81}}{\sqrt[3]{8} \sqrt{36}}$

Studdy Solution

STEP 1

1. We are given the expression $\frac{\sqrt{81}}{\sqrt[3]{8} \sqrt{36}}$ .
2. We need to simplify this expression using properties of exponents and roots.

STEP 2

1. Simplify the numerator.
2. Simplify the denominator.
3. Simplify the entire expression.

STEP 3

Simplify the numerator $\sqrt{81}$ .
$\sqrt{81} = 9$

STEP 4

Simplify the cube root in the denominator $\sqrt[3]{8}$ .
$\sqrt[3]{8} = 2$

STEP 5

Simplify the square root in the denominator $\sqrt{36}$ .
$\sqrt{36} = 6$

STEP 6

Substitute the simplified values back into the expression.
$\frac{9}{2 \times 6}$

STEP 7

Calculate the product in the denominator.
$2 \times 6 = 12$

STEP 8

Simplify the entire expression.
$\frac{9}{12} = \frac{3}{4}$
The simplified expression is:
$\boxed{\frac{3}{4}}$

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Question $\frac{\sqrt{81}}{\sqrt[3]{8} \sqrt{36}}$

Studdy Solution

STEP 1

1. We are given the expression $\frac{\sqrt{81}}{\sqrt[3]{8} \sqrt{36}}$ .
2. We need to simplify this expression using properties of exponents and roots.

STEP 2

1. Simplify the numerator.
2. Simplify the denominator.
3. Simplify the entire expression.

STEP 3

Simplify the numerator $\sqrt{81}$ .
$\sqrt{81} = 9$

STEP 4

Simplify the cube root in the denominator $\sqrt[3]{8}$ .
$\sqrt[3]{8} = 2$

STEP 5

Simplify the square root in the denominator $\sqrt{36}$ .
$\sqrt{36} = 6$

STEP 6

Substitute the simplified values back into the expression.
$\frac{9}{2 \times 6}$

STEP 7

Calculate the product in the denominator.
$2 \times 6 = 12$

STEP 8

Simplify the entire expression.
$\frac{9}{12} = \frac{3}{4}$
The simplified expression is:
$\boxed{\frac{3}{4}}$

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Question818336\frac{\sqrt{81}}{\sqrt[3]{8} \sqrt{36}}38​36​81​​

Studdy Solution

STEP 1

1. We are given the expression 818336\frac{\sqrt{81}}{\sqrt[3]{8} \sqrt{36}}38​36​81​​.2. We need to simplify this expression using properties of exponents and roots.

STEP 2

1. Simplify the numerator.2. Simplify the denominator.3. Simplify the entire expression.

STEP 3

Simplify the numerator 81\sqrt{81}81​.81=9\sqrt{81} = 981​=9

STEP 4

Simplify the cube root in the denominator 83\sqrt[3]{8}38​.83=2\sqrt[3]{8} = 238​=2

STEP 5

Simplify the square root in the denominator 36\sqrt{36}36​.36=6\sqrt{36} = 636​=6

STEP 6

Substitute the simplified values back into the expression.92×6\frac{9}{2 \times 6}2×69​

STEP 7

Calculate the product in the denominator.2×6=122 \times 6 = 122×6=12

STEP 8

Simplify the entire expression.912=34\frac{9}{12} = \frac{3}{4}129​=43​ The simplified expression is:34\boxed{\frac{3}{4}}43​​

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Question $\frac{\sqrt{81}}{\sqrt[3]{8} \sqrt{36}}$

1. We are given the expression $\frac{\sqrt{81}}{\sqrt[3]{8} \sqrt{36}}$ .
2. We need to simplify this expression using properties of exponents and roots.

1. Simplify the numerator.
2. Simplify the denominator.
3. Simplify the entire expression.

Simplify the numerator $\sqrt{81}$ .
$\sqrt{81} = 9$

Simplify the cube root in the denominator $\sqrt[3]{8}$ .
$\sqrt[3]{8} = 2$

Simplify the square root in the denominator $\sqrt{36}$ .
$\sqrt{36} = 6$

Substitute the simplified values back into the expression.
$\frac{9}{2 \times 6}$

Calculate the product in the denominator.
$2 \times 6 = 12$

Simplify the entire expression.
$\frac{9}{12} = \frac{3}{4}$
The simplified expression is:
$\boxed{\frac{3}{4}}$