# Math Help - Properties of radicals exponents

1. ## Properties of radicals exponents

Q1) 48x²

Q2) ³√ 54x^6

(all the integers are inside the square root )
Thank you,

2. Originally Posted by mj.alawami
Q1) 48x²

Q2) ³√ 54x^6

(all the integers are inside the square root )
Thank you,
$\sqrt{48 x^2} = \sqrt{16x^2 \cdot 3} = \sqrt{(4x)^2 \cdot 3}$ ....... I'll leave the rest for you

$\sqrt[3]{54x^6} = \sqrt[3]{27x^6 \cdot 2} = \sqrt[3]{(3x^2)^3 \cdot 2}$ ....... I'll leave the rest for you

3. Is this equation correct

Why can't it be =x^3/1 since there is no value before the square root

Thank you again

4. Originally Posted by mj.alawami
Is this equation correct

Why can't it be =x^3/1 since there is no value before the square root
1. The equation is true.

2. $\sqrt{\ \ \ }$ is the short form of $\sqrt[2]{\ \ \ }$

5. Originally Posted by earboth
1. The equation is true.

2. $\sqrt{\ \ \ }$ is the short form of $\sqrt[2]{\ \ \ }$
One final thing can you please convert the equations you sloved using fractions (So it will be easier for me to understand )

Thank you very much,I really appreciate it

6. Originally Posted by mj.alawami
One final thing can you please convert the equations you sloved using fractions (So it will be easier for me to understand )

Thank you very much,I really appreciate it
I'm not sure what you mean. There aren't any fractions involved. You only can convert the root sign into a rational exponent:

$
\sqrt{48 x^2} = \sqrt{16x^2 \cdot 3} = \sqrt{(4x)^2 \cdot 3} = \left((4x)^2 \cdot 3 \right)^{\frac12}
$

To change a cube root into a rational exponent use $\frac13$