Simplify the Radical Expression (5 square root of 63)÷6 square root of 7

$5 \sqrt{63} \div 6 \sqrt{7}$

Simplify the numerator.

Rewrite $63$ as $3^{2} \cdot 7$ .

Factor $9$ out of $63$ .

$5 \sqrt{9 (7)} \div 6 \sqrt{7}$

Rewrite $9$ as $3^{2}$ .

$5 \sqrt{3^{2} \cdot 7} \div 6 \sqrt{7}$

Pull terms out from under the radical.

$5 (| 3 | \sqrt{7}) \div 6 \sqrt{7}$

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$5 \cdot 3 \sqrt{7} \div 6 \sqrt{7}$

Multiply $5$ by $3$ .

$15 \sqrt{7} \div 6 \sqrt{7}$

Rewrite the division as a fraction.

$\frac{15 \sqrt{7}}{6} \sqrt{7}$

Cancel the common factor of $15$ and $6$ .

Factor $3$ out of $15 \sqrt{7}$ .

$\frac{3 (5 \sqrt{7})}{6} \sqrt{7}$

Cancel the common factors.

Factor $3$ out of $6$ .

$\frac{3 (5 \sqrt{7})}{3 (2)} \sqrt{7}$

Cancel the common factor.

$\frac{3 (5 \sqrt{7})}{3 \cdot 2} \sqrt{7}$

Rewrite the expression.

$\frac{5 \sqrt{7}}{2} \sqrt{7}$

Multiply $\frac{5 \sqrt{7}}{2} \sqrt{7}$ .

Combine $\frac{5 \sqrt{7}}{2}$ and $\sqrt{7}$ .

$\frac{5 \sqrt{7} \sqrt{7}}{2}$

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

$\frac{5 ({\sqrt{7}}^{1} \sqrt{7})}{2}$

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

$\frac{5 ({\sqrt{7}}^{1} {\sqrt{7}}^{1})}{2}$

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

$\frac{5 {\sqrt{7}}^{1 + 1}}{2}$

Add $1$ and $1$ .

$\frac{5 {\sqrt{7}}^{2}}{2}$

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

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

$\frac{5 {(7^{\frac{1}{2}})}^{2}}{2}$

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

$\frac{5 \cdot 7^{\frac{1}{2} \cdot 2}}{2}$

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

$\frac{5 \cdot 7^{\frac{2}{2}}}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{5 \cdot 7^{\frac{2}{2}}}{2}$

Rewrite the expression.

$\frac{5 \cdot 7^{1}}{2}$

Evaluate the exponent.

$\frac{5 \cdot 7}{2}$

Multiply $5$ by $7$ .

$\frac{35}{2}$

Simplify the Radical Expression (5 square root of 63)÷6 square root of 7

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