Examples with solutions for Root of a Root: Applying the formula

Exercise #1

Solve the following exercise:

11010= \sqrt[10]{\sqrt[10]{1}}=

Video Solution

Answer

All answers are correct.

Exercise #2

Solve the following exercise:

8= \sqrt[]{\sqrt{8}}=

Video Solution

Answer

814 8^{\frac{1}{4}}

Exercise #3

Solve the following exercise:

26= \sqrt[6]{\sqrt{2}}=

Video Solution

Answer

212 \sqrt[12]{2}

Exercise #4

Solve the following exercise:

12= \sqrt{\sqrt{12}}=

Video Solution

Answer

124 \sqrt[4]{12}

Exercise #5

Solve the following exercise:

535= \sqrt[5]{\sqrt[3]{5}}=

Video Solution

Answer

515 \sqrt[15]{5}

Exercise #6

Solve the following exercise:

2= \sqrt{\sqrt{2}}=

Video Solution

Answer

24 \sqrt[4]{2}

Exercise #7

Solve the following exercise:

4= \sqrt{\sqrt{4}}=

Video Solution

Answer

2 \sqrt{2}

Exercise #8

Solve the following exercise:

26= \sqrt[6]{\sqrt{2}}=

Video Solution

Answer

212 \sqrt[12]{2}

Exercise #9

Solve the following exercise:

10245= \sqrt[5]{\sqrt[]{1024}}=

Video Solution

Answer

2

Exercise #10

Solve the following exercise:

643= \sqrt[3]{\sqrt{64}}=

Video Solution

Answer

2

Exercise #11

Solve the following exercise:

7293= \sqrt[3]{\sqrt{729}}=

Video Solution

Answer

3

Exercise #12

Solve the following exercise:

625= \sqrt{\sqrt{625}}=

Video Solution

Answer

5

Exercise #13

Solve the following exercise:

51233= \sqrt[3]{\sqrt[3]{512}}=

Video Solution

Answer

2

Exercise #14

Solve the following exercise:

1634= \sqrt[4]{\sqrt[3]{16}}=

Video Solution

Answer

Answers a and b are correct

Exercise #15

Complete the following exercise:

363= \sqrt[3]{\sqrt{36}}=

Video Solution

Answer

3616 36^{\frac{1}{6}}

Exercise #16

Solve the following exercise:

100510= \sqrt[10]{\sqrt[5]{100}}=

Video Solution

Answer

10050 \sqrt[50]{100}

Exercise #17

Solve the following exercise:

1443= \sqrt[3]{\sqrt{144}}=

Video Solution

Answer

1446 \sqrt[6]{144}

Exercise #18

Solve the following exercise:

27= \sqrt[7]{\sqrt{2}}=

Video Solution

Answer

214 \sqrt[14]{2}

Exercise #19

Solve the following exercise:

1447= \sqrt[7]{\sqrt[4]{14}}=

Video Solution

Answer

1428 \sqrt[28]{14}

Exercise #20

Solve the following exercise:

64= \sqrt[4]{\sqrt{6}}=

Video Solution

Answer

68 \sqrt[8]{6}