Simplify 7/16 square root of 64/7

$\frac{7}{16} \sqrt{\frac{64}{7}}$

Step 1

Rewrite $\sqrt{\frac{64}{7}}$ as $\frac{\sqrt{64}}{\sqrt{7}}$ .

$\frac{7}{16} \cdot \frac{\sqrt{64}}{\sqrt{7}}$

Step 2

Simplify the numerator.

Rewrite $64$ as $8^{2}$ .

$\frac{7}{16} \cdot \frac{\sqrt{8^{2}}}{\sqrt{7}}$

Pull terms out from under the radical, assuming positive real numbers.

$\frac{7}{16} \cdot \frac{8}{\sqrt{7}}$

Step 3

Simplify terms.

Cancel the common factor of $8$ .

Factor $8$ out of $16$ .

$\frac{7}{8 (2)} \cdot \frac{8}{\sqrt{7}}$

Cancel the common factor.

$\frac{7}{8 \cdot 2} \cdot \frac{8}{\sqrt{7}}$

Rewrite the expression.

$\frac{7}{2} \cdot \frac{1}{\sqrt{7}}$

Multiply $\frac{7}{2}$ by $\frac{1}{\sqrt{7}}$ .

$\frac{7}{2 \sqrt{7}}$

Step 4

Multiply $\frac{7}{2 \sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$\frac{7}{2 \sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}}$

Step 5

Combine and simplify the denominator.

Multiply $\frac{7}{2 \sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$\frac{7 \sqrt{7}}{2 \sqrt{7} \sqrt{7}}$

Move $\sqrt{7}$ .

$\frac{7 \sqrt{7}}{2 (\sqrt{7} \sqrt{7})}$

Raise $\sqrt{7}$ to the power of $1$ .

$\frac{7 \sqrt{7}}{2 ({\sqrt{7}}^{1} \sqrt{7})}$

Raise $\sqrt{7}$ to the power of $1$ .

$\frac{7 \sqrt{7}}{2 ({\sqrt{7}}^{1} {\sqrt{7}}^{1})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{7 \sqrt{7}}{2 {\sqrt{7}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{7 \sqrt{7}}{2 {\sqrt{7}}^{2}}$

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$\frac{7 \sqrt{7}}{2 {(7^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{7 \sqrt{7}}{2 \cdot 7^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{7 \sqrt{7}}{2 \cdot 7^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{7 \sqrt{7}}{2 \cdot 7^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{7 \sqrt{7}}{2 \cdot 7^{1}}$

Evaluate the exponent.

$\frac{7 \sqrt{7}}{2 \cdot 7}$

Step 6

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 \sqrt{7}}{2 \cdot 7}$

Rewrite the expression.

$\frac{\sqrt{7}}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{7}}{2}$

Decimal Form:

$1.32287565 \dots$

Simplify 7/16 square root of 64/7

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