Simplify square root of x(5 square root of x-2 square root of x)

$\sqrt{x} (5 \sqrt{x} - 2 \sqrt{x})$

Step 1

Subtract $2 \sqrt{x}$ from $5 \sqrt{x}$ .

$\sqrt{x} (3 \sqrt{x})$

Step 2

Rewrite using the commutative property of multiplication.

$3 \sqrt{x} \sqrt{x}$

Step 3

Multiply $3 \sqrt{x} \sqrt{x}$ .

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

$3 ({\sqrt{x}}^{1} \sqrt{x})$

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

$3 ({\sqrt{x}}^{1} {\sqrt{x}}^{1})$

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

$3 {\sqrt{x}}^{1 + 1}$

Add $1$ and $1$ .

$3 {\sqrt{x}}^{2}$

Step 4

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

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

$3 {(x^{\frac{1}{2}})}^{2}$

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

$3 x^{\frac{1}{2} \cdot 2}$

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

$3 x^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$3 x^{\frac{2}{2}}$

Rewrite the expression.

$3 x^{1}$

Simplify.

$3 x$