How do you simplify $\sqrt{\frac{100}{3}}$ $sqrt(100/3)$ ?

Question

How do you simplify $\sqrt{\frac{100}{3}}$ $sqrt(100/3)$ ?

1 Answer

Impact of this question

5295 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-11T13:37:31

$\frac{10 \sqrt{3}}{3}$ $(10sqrt3)/3$

Explanation:

$using the law of radicals$ $"using the "color(blue)"law of radicals"$

$∙ x \sqrt{\frac{a}{b}} \Leftrightarrow \frac{\sqrt{a}}{\sqrt{b}}$ $•color(white)(x)sqrt(a/b)hArrsqrta/sqrtb$

$∙ x \sqrt{a} \times \sqrt{a} = a$ $•color(white)(x)sqrtaxxsqrta=a$

$\Rightarrow \sqrt{\frac{100}{3}} = \frac{\sqrt{100}}{\sqrt{3}} = \frac{10}{\sqrt{3}}$ $rArrsqrt(100/3)=sqrt100/sqrt3=10/sqrt3$

$rationalise the denominator$ $color(blue)"rationalise the denominator"$

$multiply numerator/denominator by \sqrt{3}$ $"multiply numerator/denominator by "sqrt3$

$\Rightarrow \frac{10 \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}} = \frac{10 \sqrt{3}}{3}$ $rArr(10xxsqrt3)/(sqrt3xxsqrt3)=(10sqrt3)/3$

$\Rightarrow \sqrt{\frac{100}{3}} = \frac{10 \sqrt{3}}{3} \leftarrow in simplified form$ $rArrsqrt(100/3)=(10sqrt3)/3larrcolor(blue)"in simplified form"$

Science

Math

Humanities

... and beyond

How do you simplify $\sqrt{\frac{100}{3}}$ $sqrt(100/3)$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you simplify √1003sqrt(100/3)?

1 Answer

Explanation:

Related questions

Impact of this question

How do you simplify $\sqrt{\frac{100}{3}}$ $sqrt(100/3)$ ?