How do you simplify the expression $2 \sqrt{\frac{1}{2}} + 2 \sqrt{2} - \sqrt{8}$ $2sqrt(1/2)+2sqrt2-sqrt8$ ?

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How do you simplify the expression $2 \sqrt{\frac{1}{2}} + 2 \sqrt{2} - \sqrt{8}$ $2sqrt(1/2)+2sqrt2-sqrt8$ ?

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Answer 1 · 2017-05-07T02:32:20

$2 \sqrt{\frac{1}{2}} + 2 \sqrt{2} - \sqrt{8} = \sqrt{2}$ $2sqrt(1/2)+2sqrt2-sqrt8=color(blue)(sqrt2$

Explanation:

Simplify.

$2 \sqrt{\frac{1}{2}} + 2 \sqrt{2} - \sqrt{8}$ $2sqrt(1/2)+2sqrt2-sqrt8$

In order to add or subtract numbers with square roots, the square roots must be the same.

Simplify $\sqrt{8}$ $sqrt8$ by prime factorization.

$2 \sqrt{\frac{1}{2}} + 2 \sqrt{2} - \sqrt{2 \times 2 \times 2}$ $2sqrt(1/2)+2sqrt2-sqrt(2xx2xx2)$

$2 \sqrt{\frac{1}{2}} + 2 \sqrt{2} - \sqrt{2^{2} \times 2}$ $2sqrt(1/2)+2sqrt2-sqrt(2^2xx2)$

$2 \sqrt{\frac{1}{2}} + 2 \sqrt{2} - 2 \sqrt{2}$ $2sqrt(1/2)+2sqrt2-2sqrt2$

Simplify $\sqrt{\frac{1}{2}}$ $sqrt(1/2)$ to $\frac{\sqrt{1}}{\sqrt{2}}$ $(sqrt1)/(sqrt2)$ .

$2 \times \frac{\sqrt{1}}{\sqrt{2}} + 2 \sqrt{2} - 2 \sqrt{2}$ $2xx(sqrt1)/(sqrt2)+2sqrt2-2sqrt2$

Simplify $\sqrt{1}$ $sqrt1$ to $1$ $1$ .

$2 \times \frac{1}{\sqrt{2}} + 2 \sqrt{2} - 2 \sqrt{2}$ $2xx1/(sqrt2)+2sqrt2-2sqrt2$

Rationalize the denominator by multiplying the numerator and denominator by $\sqrt{2}$ $color(red)(sqrt2$ .

$2 \times \frac{1}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} + 2 \sqrt{2} - 2 \sqrt{2}$ $2xx1/(sqrt2)xxcolor(red)(sqrt2)/color(red)(sqrt2)+2sqrt2-2sqrt2$

Simplify.

$\frac{2 \times \sqrt{2}}{\sqrt{2} \times \sqrt{2}} + 2 \sqrt{2} - 2 \sqrt{2}$ $(2xxsqrt2)/(sqrt2xxsqrt2)+2sqrt2-2sqrt2$

Simplify.

$\frac{2 \sqrt{2}}{2} + 2 \sqrt{2} - 2 \sqrt{2}$ $(2sqrt2)/2+2sqrt2-2sqrt2$

Cancel the $\frac{2}{2}$ $2/2$ .

$(color(red)cancel(color(black)(2))sqrt2)/color(red)cancel(color(black)(2))+2sqrt2-2sqrt2$

$sqrt2+2sqrt2-2sqrt2$

Simplify.

$3sqrt2-2sqrt2$

Answer.

$sqrt2$

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How do you simplify the expression $2 \sqrt{\frac{1}{2}} + 2 \sqrt{2} - \sqrt{8}$ $2sqrt(1/2)+2sqrt2-sqrt8$ ?

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Explanation:

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How do you simplify the expression 2sqrt(1/2)+2sqrt2-sqrt82√12+2√2−√82sqrt(1/2)+2sqrt2-sqrt8?

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How do you simplify the expression $2 \sqrt{\frac{1}{2}} + 2 \sqrt{2} - \sqrt{8}$ $2sqrt(1/2)+2sqrt2-sqrt8$ ?