Updated: 06 Aug 2023

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Mathematics sometimes feels like a magical world full of interesting symbols and concepts. One such symbol that you might have come across is the radical sign ( \sqrt{ \quad } ) . The radical sign ( \sqrt{ \quad } ) might look like a simple little symbol, but it holds a significant role in mathematics.
So, embrace the power of radicals, and let them guide you through the captivating landscapes of algebra and beyond.

##### Table of Content

1. In \sqrt[n]{a},\ then \ \sqrt{ \quad } is called
O Index
O All of them

Explanation:

2. In \sqrt[n]{a}, \ then \ a is called
O Index
O All of them

Explanation:

3. In \sqrt[n]{a}, \ then \ n is called
O Index
O All of them

Index
Explanation:

4. The exponential form of \sqrt[n]{a} is
O a^n
O a^2
O a^{\frac{2}{n}}
O a^{\frac{1}{n}}

a^{\frac{1}{n}}
Explanation:
It is the General Exponential form of any radical form

5. \sqrt{2} , the index is
O 0
O 1
O 2
O All of them

2
Explanation:
If the index is not given means it is 2 which we cannot write.

6. \sqrt{1}=
O 1
O 0
O -1
O 2

1
Explanation:
Square root of 1 will always be 1.

7. \sqrt[3]{1}=
O 1
O 0
O -1
O 2

1
Explanation:
Cube root of 1 will always be 1

8. \sqrt[3]{1}=
O 1
O 0
O -1
O 2

1
Explanation:
Forth root of 1 will always be 1.

9. \sqrt{36}=
O 6
O 0
O -6
O 4

6
Explanation:
\sqrt{36}=\sqrt{6^2}
\sqrt{36}=(6^2)^\frac{1}{2}
\sqrt{36}=6

10. \sqrt[3]{216}=
O 4
O 5
O 6
O 7

6
Explanation:
\sqrt[3]{216}=\sqrt[3]{6^3}
\sqrt[3]{216}=(6^3)^\frac{1}{3}
\sqrt[3]{216}=6

11. \sqrt[4]{256}=
O 4
O 5
O 6
O 7

4
Explanation:
\sqrt[4]{256}=\sqrt[4]{4^4}
\sqrt[4]{256}=(4^4)^\frac{1}{4}
\sqrt[4]{256}=4

12. \sqrt[4]{625}=
O 4
O 5
O 6
O 7

5
Explanation:
\sqrt[4]{625}=\sqrt[4]{5^4}
\sqrt[4]{625}=(5^4)^\frac{1}{4}
\sqrt[4]{625}=5

13. \sqrt[4]{1296}=
O 4
O 5
O 6
O 7

6
Explanation:
\sqrt[4]{1296}=\sqrt[4]{6^4}
\sqrt[4]{1296}=(6^4)^\frac{1}{4}
\sqrt[4]{1296}=6

14. If x^2=16 , then x=
O 4
O -4
O Both a & b
O None of these

Both a & b
Explanation:
This means what numbers squared becomes 16. Thus x \ can \ be \ 4 \ or \ -4 \ like \ (4)^2=16 \ and \ also \ (-4)^2=16.
Hence the value of x=\pm 4 .

15. If x=\sqrt{16} , then x=
O 4
O -4
O Both a & b
O None of these

4
Explanation:
Here x is the principal square root of 16, which has always a positive value such is x=4 .

16. \sqrt[4]{1296} is called root
O 4^{th}
O 5^{th}
O 2^{nd}
O Square

4^{th}
Explanation:
Here is the index of 4, thus it is called 4^{th} root.

17. \sqrt[3]{64}=
O 4
O -4
O Imaginary
O None of these

4
Explanation:
\sqrt[3]{64}=\sqrt[3]{4^3}
\sqrt[3]{64}=(4^3)^\frac{1}{3}
\sqrt[3]{64}=4

18. \sqrt[3]{-64}=
O 4
O -4
O Imaginary
O None of these

-4
Explanation:
If a is negative, then n must be odd for the nth root of a to be a real number.
\sqrt[3]{-64}=\sqrt[3]{(-4)^3}
\sqrt[3]{-64}=\left[(-4)^3\right]^\frac{1}{3}
\sqrt[3]{-64}=-4

19. \sqrt{-64}=
O 4
O -4
O Imaginary
O None of these

Imaginary
Explanation:
If radicand is negative, then index must be odd, here the index is 2 which is even.
Hence, \sqrt{-64}= imaginary

20. \sqrt[n]{0}=
O 1
O 0
O n
O -0

0
Explanation:
If a is zero, then
\sqrt[n]{0}=0

21. \sqrt[n]{ab}=
O \sqrt[n]{a} \cdot \sqrt[n]{b}
O \sqrt[n]{a}+\sqrt[n]{b}
O \sqrt[n]{a} \cdot \sqrt{b}
O \sqrt{a} \cdot \sqrt[n]{b}

\sqrt[n]{a} \cdot \sqrt[n]{b}
Explanation:
It is the product rule of Radical.

22. \sqrt[n]{\frac{a}{b}}=
O \sqrt[n]{a} \cdot \sqrt[n]{b}
O \sqrt[n]{a}+\sqrt[n]{b}
O \sqrt[n]{a}-\sqrt[n]{b}
O \frac{\sqrt[n]{a}}{\sqrt[n]{b}}

\frac{\sqrt[n]{a}}{\sqrt[n]{b}}
Explanation:
It is the Quotient rule of Radicand.

23. 2 \sqrt{\frac{150 x y}{3 x}}=
O 2 \sqrt{y}
O 10 \sqrt{y}
O 2 \sqrt{2 y}
O 10 \sqrt{2 y}

10 \sqrt{2 y}
Explanation:
2 \sqrt{\frac{150 x y}{3 x}}=2 \sqrt{50y}
2 \sqrt{\frac{150 x y}{3 x}}=2 \sqrt{25 \times 2y}
2 \sqrt{\frac{150 x y}{3 x}}=2 \times 5 \sqrt{2y}
2 \sqrt{\frac{150 x y}{3 x}}=10 \sqrt{2y}

24. \sqrt[n]{a}=
O a^{\frac{m}{n}}
O a^{\frac{1}{n}}
O a^{\frac{n}{m}}
O All of them

a^{\frac{1}{n}}
Explanation:
It is the exponential form of radical.

25. a^{\frac{m}{n}}=
O \sqrt[n]{a}
O \sqrt[n]{a^m}
O Both a & b
O None of these

\sqrt[n]{a^m}
Explanation:
a^{\frac{m}{n}}=(a^m)^\frac{1}{n}
a^{\frac{m}{n}}=\sqrt[n]{a^m}

26. \sqrt{13} is ________ form
O Exponential
O Cubic

Explanation:
This is the way to represent the radical form.

27. 13^2 is ________ form.
O Exponential
O Cubic

Exponential
Explanation:
This is the way to represent the Exponential form.

28. 2^4=
O 16
O -16
O Both a & b
O None of these

16
Explanation:
2^4= 2 \times 2 \times 2 \times 2
2^4= 16

29. -2^4=
O 16
O -16
O Both a & b
O None of these

-16
Explanation:
-2^4= -(2 \times 2 \times 2 \times 2)
-2^4= -16

30. (-2)^4=
O 16
O -16
O Both a & b
O None of these

16
Explanation:
(-2)^4= -2 \times -2 \times -2 \times -2
(-2)^4= 16

31. \sqrt[n]{a^m}=
O a^{\frac{m}{n}}
O a^{\frac{1}{n}}
O a^{\frac{n}{m}}
O All of them