Properties of radicals exponents

**mj.alawami** · January 27th 2009, 07:34 AM

Q1)

48x²

Q2) ³√ 54x^6

(all the integers are inside the square root )
Please answer them in steps
Thank you,

**earboth** · January 27th 2009, 07:39 AM

Originally Posted by mj.alawami

Q1)

48x²

Q2) ³√ 54x^6

(all the integers are inside the square root )
Please answer them in steps
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

**mj.alawami** · January 27th 2009, 07:47 AM

Is this equation correct

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

Sorry,but can you please convert your working using fractions?
Thank you again

**earboth** · January 27th 2009, 07:56 AM

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 $\sqrt[2]{\ \ \ }$

**mj.alawami** · January 27th 2009, 07:59 AM

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

**earboth** · January 27th 2009, 08:10 AM

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:

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

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

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