Question #2bca3

Question

Question #2bca3

2 Answers

Impact of this question

1199 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-11-19T01:38:21

See below

Explanation:

Laws:
1) $x^{\frac{1}{2}} = \sqrt{x} \Leftrightarrow \sqrt{x} = x^{\frac{1}{2}}$ $x^(1/2)=sqrt(x) iff sqrt(x)=x^(1/2)$
2) $x^{a} \cdot x^{b} = x^{a + b} \Leftrightarrow x^{a + b} = x^{a} \cdot x^{b}$ $x^a*x^b=x^(a+b) iff x^(a+b)=x^a*x^b$
2) $\frac{x^{a}}{x^{b}} = x^{a - b}$ $x^a/x^b=x^(a-b)$

$\frac{2}{\sqrt{2}} = ?$ $2/sqrt(2)=?$

First:
$2 = 2^{1}$ $2=2^1$
$\Rightarrow 2^{1} = 2^{(\frac{1}{2} + \frac{1}{2})}$ $=> 2^1=2^((1/2+1/2))$
$\Rightarrow 2^{\frac{1}{2} + \frac{1}{2}} = 2^{\frac{1}{2}} \cdot 2^{\frac{1}{2}}$ $=> 2^(1/2+1/2)=2^(1/2)*2^(1/2)$

Second:
$2^{\frac{1}{2}} \Leftrightarrow \sqrt{2}$ $2^(1/2) iff sqrt(2)$

and therefore:
$\frac{2}{\sqrt{2}} = \frac{2^{\frac{1}{2}} \cdot 2^{\frac{1}{2}}}{2^{\frac{1}{2}}} = 2^{\frac{1}{2}} = \sqrt{2}$ $2/sqrt(2)=(2^(1/2)*2^(1/2))/(2^(1/2))=2^(1/2)=sqrt(2)$

Answer 2 · 2017-11-19T01:44:55

See below.

Explanation:

$\frac{2}{\sqrt{2}}$ $2/sqrt2$ has a radical in its denominator. If we want to remove the radical, we can multiply the expression by $\frac{\sqrt{2}}{\sqrt{2}}$ $sqrt2/sqrt2$ . This is essentially the same as multiplying by $1$ $1$ , so we aren't changing the value of the expression.

$\frac{2}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}$ $2/sqrt2 *sqrt2/sqrt2$

$\sqrt{2} \cdot \sqrt{2}$ $sqrt2 * sqrt2$ is simply $2$ $2$ . Thus, we have

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

We can now cancel the $2$ $2$ in the numerator and denominator.

$(cancel2sqrt2) / cancel2 = sqrt2$

Science

Math

Humanities

... and beyond

Question #2bca3

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question