Examples with solutions for Root of a Root: Number of terms

Exercise #1

Complete the following exercise:

16316= \sqrt[3]{\sqrt{16}}\cdot\sqrt[]{\sqrt{16}}=

Video Solution

Answer

16512 16^{\frac{5}{12}}

Exercise #2

Complete the following exercise:

42= \sqrt{\sqrt{4}}\cdot\sqrt{\sqrt{2}}=

Video Solution

Answer

2142 2^{\frac{1}{4}}\sqrt{2}

Exercise #3

Complete the following exercise:

4916= \sqrt{\sqrt{49}}\cdot\sqrt{\sqrt{16}}=

Video Solution

Answer

27 2\sqrt{7}

Exercise #4

Complete the following exercise:

25253= \sqrt{25}\cdot\sqrt[3]{\sqrt{25}}=

Video Solution

Answer

5113 5^{1\frac{1}{3}}

Exercise #5

Complete the following exercise:

168= \sqrt{\sqrt{16}}\cdot\sqrt{\sqrt{8}}=

Video Solution

Answer

1284 \sqrt[4]{128}

Exercise #6

Complete the following exercise:

24= \sqrt{\sqrt{2}}\cdot\sqrt{\sqrt{4}}=

Video Solution

Answer

84 \sqrt[4]{8}

Exercise #7

Complete the following exercise:

253643= \sqrt[3]{\sqrt{25}}\cdot\sqrt[3]{\sqrt{64}}=

Video Solution

Answer

253 2\sqrt[3]{5}

Exercise #8

Complete the following exercise:

3536= \sqrt[5]{\sqrt{3}}\cdot\sqrt[6]{\sqrt{3}}=

Video Solution

Answer

3110+112 3^{\frac{1}{10}+\frac{1}{12}}

Exercise #9

Complete the following exercise:

3343= \sqrt[3]{\sqrt{3}}\cdot\sqrt[3]{\sqrt{4}}=

Video Solution

Answer

126 \sqrt[6]{12}

Exercise #10

Complete the following exercise:

3535= \sqrt[5]{\sqrt{3}}\cdot\sqrt[5]{\sqrt{3}}=

Video Solution

Answer

910 \sqrt[10]{9}

Exercise #11

Complete the following exercise:

643643= \sqrt[3]{\sqrt{64}}\cdot\sqrt[3]{64}=

Video Solution

Answer

8

Exercise #12

Complete the following exercise:

6461634= \sqrt[6]{\sqrt{64}}\cdot\sqrt[4]{\sqrt[3]{16}}=

Video Solution

Answer

102412 \sqrt[12]{1024}