# How do you simplify sqrt( 3/10) *sqrt(5/8)?

Jan 24, 2016

$\frac{\sqrt{3}}{4}$
or $0.433$

#### Explanation:

$\sqrt{\frac{3}{10}} . \sqrt{\frac{5}{8}}$

Since both fractions are square roots, therefore, taking both fractions under the same root sign

$\sqrt{\frac{3}{10.} \frac{5}{8}}$
or simplifying we obtain $\sqrt{\frac{3}{\cancel{10}} _ 2. {\cancel{5}}^{1} / 8}$
$= \sqrt{\frac{3}{2.} \frac{1}{8}}$
Multiplying the numerators and denominators respectively
$= \sqrt{\frac{3}{16}}$
Now we know that $\sqrt{16} = 4$, we obtain
$= \frac{\sqrt{3}}{4}$
Inserting the value of $\sqrt{3} = 1.732$ in the numerator and dividing with the denominator, we obtain

Jan 24, 2016

$\frac{1}{4} \sqrt{3}$

#### Explanation:

Using the following :

 • sqrta xx sqrtb = sqrtab hArr sqrtab = sqrta xx sqrtb

 sqrt( 3/10). sqrt(5/8) = sqrt(3/10 xx 5/8) = sqrt(15/80

$= \sqrt{\frac{3}{16}} = \frac{\sqrt{3}}{\sqrt{16}} = \frac{\sqrt{3}}{4} = \frac{1}{4} \sqrt{3}$