Simplify the Radical Expression 1/2 square root of 4x-1/3 square root of 9x+1/4 square root of 64

$\frac{1}{2} \sqrt{4 x} - \frac{1}{3} \sqrt{9 x} + \frac{1}{4} \sqrt{64}$

Step 1

Simplify each term.

Rewrite $4$ as $2^{2}$ .

$\frac{1}{2} \sqrt{2^{2} x} - \frac{1}{3} \sqrt{9 x} + \frac{1}{4} \sqrt{64}$

Pull terms out from under the radical.

$\frac{1}{2} (| 2 | \sqrt{x}) - \frac{1}{3} \sqrt{9 x} + \frac{1}{4} \sqrt{64}$

Remove non-negative terms from the absolute value.

$\frac{1}{2} (2 \sqrt{x}) - \frac{1}{3} \sqrt{9 x} + \frac{1}{4} \sqrt{64}$

Cancel the common factor of $2$ .

Factor $2$ out of $2 \sqrt{x}$ .

$\frac{1}{2} (2 (\sqrt{x})) - \frac{1}{3} \sqrt{9 x} + \frac{1}{4} \sqrt{64}$

Cancel the common factor.

$\frac{1}{2} (2 \sqrt{x}) - \frac{1}{3} \sqrt{9 x} + \frac{1}{4} \sqrt{64}$

Rewrite the expression.

$\sqrt{x} - \frac{1}{3} \sqrt{9 x} + \frac{1}{4} \sqrt{64}$

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

$\sqrt{x} - \frac{1}{3} \sqrt{3^{2} x} + \frac{1}{4} \sqrt{64}$

Pull terms out from under the radical.

$\sqrt{x} - \frac{1}{3} (| 3 | \sqrt{x}) + \frac{1}{4} \sqrt{64}$

Remove non-negative terms from the absolute value.

$\sqrt{x} - \frac{1}{3} (3 \sqrt{x}) + \frac{1}{4} \sqrt{64}$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$\sqrt{x} + \frac{- 1}{3} (3 \sqrt{x}) + \frac{1}{4} \sqrt{64}$

Factor $3$ out of $3 \sqrt{x}$ .

$\sqrt{x} + \frac{- 1}{3} (3 (\sqrt{x})) + \frac{1}{4} \sqrt{64}$

Cancel the common factor.

$\sqrt{x} + \frac{- 1}{3} (3 \sqrt{x}) + \frac{1}{4} \sqrt{64}$

Rewrite the expression.

$\sqrt{x} - 1 \sqrt{x} + \frac{1}{4} \sqrt{64}$

Rewrite $- 1 \sqrt{x}$ as $- \sqrt{x}$ .

$\sqrt{x} - \sqrt{x} + \frac{1}{4} \sqrt{64}$

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

$\sqrt{x} - \sqrt{x} + \frac{1}{4} \sqrt{8^{2}}$

Pull terms out from under the radical.

$\sqrt{x} - \sqrt{x} + \frac{1}{4} | 8 |$

Remove non-negative terms from the absolute value.

$\sqrt{x} - \sqrt{x} + \frac{1}{4} \cdot 8$

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$\sqrt{x} - \sqrt{x} + \frac{1}{4} \cdot (4 (2))$

Cancel the common factor.

$\sqrt{x} - \sqrt{x} + \frac{1}{4} \cdot (4 \cdot 2)$

Rewrite the expression.

$\sqrt{x} - \sqrt{x} + 2$

Step 2

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

$0 + 2$

Step 3

Add $0$ and $2$ .

$2$

Simplify the Radical Expression 1/2 square root of 4x-1/3 square root of 9x+1/4 square root of 64

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