Question

Dividing Radical Expressions
Find the value of 7 times x squared all over the square root of x to the fifth power.

please show steps and explain

Answer 1

would that be 7 square root x

Answer 2

you can use the index laws for this problem

1st part

\[\sqrt{x^5} = x^{\frac {5}{2}}\]

\[\frac{1}{\sqrt{x^5}} = x^{-\frac{5}{2}}\]
\[\frac{7x^2}{\sqrt{x^5}} = 7x^2 \times x^{-\frac{5}{2}}\]

now using the multiplication law

\[x^a \times x ^b = x^{a +b}\]

\[7 \times x^2 \times x^{-\frac{5}{2}} = 7x^{2 -\frac{5}{2}} = 7x^{-\frac{1}{2}}\]

which can be written

\[\frac{7}{\sqrt{x}}\]

by rationalising the denominator you get

\[\frac{7\sqrt{x}}{x}\]

Answer 3

thank you so much. i kinda have a stupid question but how would i find the exact value of the square root of 2 over the square root of 8.

i know square root of 8 does into 4 x 2 but does 4 break down again o does it stay the same

Answer 4

\[\frac{\sqrt{2}}{2\sqrt{2}} = = \frac{1}{2} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{1}{2}\]

Answer 5

thank you