Question

Simplify the number into simplest radical form. Use the factor tree to help determine the factors. StartRoot 96 Endroot StartRoot 6 EndRoot 2StartRoot 6 EndRoot 4StartRoot 6 EndRoot 4StartRoot 3 EndRoot

Answer 1

Answer:

$[tex]4608\sqrt{3}$[/tex]

Step-by-step explanation:

1. $\sqrt{96} *\sqrt{6}* 2*\sqrt{6}*4 *\sqrt{6} *4*\sqrt{3}$

2. $\sqrt{2^{5} *3} \sqrt{6} *2\sqrt{6}*4\sqrt{6}*4\sqrt{3}$   factoring 96

since $\sqrt{2^{5}*3 } = \sqrt{2^{5} } \sqrt{3}$

3. $\sqrt{2^{5} } \sqrt{3}\sqrt{6} *2\sqrt{6}*4\sqrt{6}*4\sqrt{3}$

using exponent rule - $(a^{b}) ^{c} = a^{bc}$

$\sqrt{2^{5} } = 2^{5/2}$

4. $2^{5/2}\sqrt{3}\sqrt{2*3} *2\sqrt{6}*4\sqrt{6}*4\sqrt{3}$

doing some simple simplification and $4=2^{2}$  and 6=2*3

5. $2^{5/2} \sqrt{3} \sqrt{2} \sqrt{3} *2\sqrt{2} \sqrt{3} *2^{2}\sqrt{2} \sqrt{3}*4\sqrt{3}$

collecting the roots on one side and applying exponent rule

6. $\sqrt{3} \sqrt{3}\sqrt{3} \sqrt{3}\sqrt{2} \sqrt{2}\sqrt{2} *2^{5/2+1+2+2} \sqrt{3}$

Applying exponents rule on all $\sqrt{3}$ and $\sqrt{2}$

7. $2^{1/2+1/2+1/2} *2^{5/2+1+2+2}*3^{1/2+1/2+1/2+1/2+1/2}$

combining all powers of 2

8. $2^{1/2+1/2+1/2+5/2+1+2+2}*3^{1/2+1/2+1/2+1/2+1/2}$

Simplifying

9. $2^{9} *3^{2}\sqrt{3}$

10. $512*9\sqrt{3}$

11. $4608\sqrt{3}$

Answer 2

Answer: 4 square root 6