Examples with solutions for Rules of Roots Combined: Solving the equation

Exercise #1

Solve the following equation:

644=2x \frac{\sqrt{64}}{\sqrt{4}}=2x

Video Solution

Answer

2

Exercise #2

98x=7 \frac{\sqrt{98}}{\sqrt{x}}=7

Video Solution

Answer

2 2

Exercise #3

Solve for x:

6x=36 \sqrt{6}x=\sqrt{36}

Video Solution

Answer

6 \sqrt{6}

Exercise #4

Solve the following equation:

90x=3 \frac{\sqrt{90}}{\sqrt{x}}=3

Video Solution

Answer

10

Exercise #5

Solve the following equation:

50x=5 \frac{\sqrt{50}}{\sqrt{x}}=5

Video Solution

Answer

Answers b and c

Exercise #6

Solve the following equation:

23=x6 \sqrt{2}\cdot\sqrt{3}=\frac{x}{\sqrt{6}}

Video Solution

Answer

6

Exercise #7

Solve for x:

205x=225 \frac{\sqrt{20}\cdot\sqrt{5}}{x}=2\cdot\sqrt{25}

Video Solution

Answer

1 1

Exercise #8

Solve for x:

8422=x2 \frac{\sqrt{8}\cdot\sqrt{4}\cdot\sqrt{2}}{\sqrt{2}}=\sqrt{x^2}

Video Solution

Answer

x=32 x=\sqrt{32}

Exercise #9

Solve the following exercise:

81=x63 \sqrt{\sqrt{81}}=\sqrt[3]{\sqrt{x^6}}

Video Solution

Answer

x=3 x=3

Exercise #10

Solve the following equation:

4510=x \frac{\sqrt{4}\cdot\sqrt{5}}{\sqrt{10}}=x

Video Solution

Answer

2 \sqrt{2}

Exercise #11

Solve for x:

4525=2x \frac{\sqrt{4}\cdot\sqrt{5}}{\sqrt{25}}=2x

Video Solution

Answer

x=2010 x=\frac{\sqrt{20}}{10}

Exercise #12

Solve for x:

2416=x8 \frac{\sqrt{2}\cdot\sqrt{4}}{\sqrt{16}}=\frac{x}{\sqrt{8}}

Video Solution

Answer

2 2

Exercise #13

Solve the following exercise:

16643=x2 \sqrt{\frac{16}{\sqrt[3]{64}}}=\sqrt{x^2}

Video Solution

Answer

x=2 x=2

Exercise #14

Solve the following exercise:

x105=81 \sqrt[5]{\sqrt[]{x^{10}}}=\sqrt{\sqrt{81}}

Video Solution

Answer

x=3 x=3

Exercise #15

Solve the following exercise:

x6=1625 \sqrt{x^6}=\sqrt{\sqrt{16}}\cdot\sqrt{25}

Video Solution

Answer

x3=10 x^3=10

Exercise #16

Solve the following exercise:

144=x10353 \sqrt{144}=\sqrt[3]{\sqrt[5]{x^{10\cdot3}}}

Video Solution

Answer

x2=12 x^2=12