Square Root of a Negative Number

There is no root of a negative number since any positive number raised to the second power will result in a positive number.

Suggested Topics to Practice in Advance

  1. Exponents and Roots - Basic
  2. Exponents and Exponent rules
  3. Basis of a power
  4. The exponent of a power
  5. Powers

Practice Square Root of a Negative Number

Examples with solutions for Square Root of a Negative Number

Exercise #1

Choose the largest value

Video Solution

Step-by-Step Solution

Let's calculate the numerical value of each of the roots in the given options:

25=516=49=3 \sqrt{25}=5\\ \sqrt{16}=4\\ \sqrt{9}=3\\ and it's clear that:

5>4>3>1 Therefore, the correct answer is option A

Answer

25 \sqrt{25}

Exercise #2

441= \sqrt{441}=

Video Solution

Step-by-Step Solution

The root of 441 is 21.

21×21= 21\times21=

21×20+21= 21\times20+21=

420+21=441 420+21=441

Answer

21 21

Exercise #3

(380.2512)211= (\sqrt{380.25}-\frac{1}{2})^2-11=

Video Solution

Step-by-Step Solution

According to the order of operations, we'll first solve the expression in parentheses:

(380.2512)=(19.512)=(19) (\sqrt{380.25}-\frac{1}{2})=(19.5-\frac{1}{2})=(19)

In the next step, we'll solve the exponentiation, and finally subtract:

(19)211=(19×19)11=36111=350 (19)^2-11=(19\times19)-11=361-11=350

Answer

350

Exercise #4

49= \sqrt{49}=

Video Solution

Answer

7

Exercise #5

36= \sqrt{36}=

Video Solution

Answer

6

Exercise #6

64= \sqrt{64}=

Video Solution

Answer

8

Exercise #7

Solve the following exercise:

x2= \sqrt{x^2}=

Video Solution

Answer

x x

Exercise #8

x=1 \sqrt{x}=1

Video Solution

Answer

1

Exercise #9

x=2 \sqrt{x}=2

Video Solution

Answer

4

Exercise #10

x=6 \sqrt{x}=6

Video Solution

Answer

36

Exercise #11

4= \sqrt{4}=

Video Solution

Answer

2

Exercise #12

9= \sqrt{9}=

Video Solution

Answer

3

Exercise #13

16= \sqrt{16}=

Video Solution

Answer

4

Exercise #14

36= \sqrt{36}=

Video Solution

Answer

6

Exercise #15

64= \sqrt{64}=

Video Solution

Answer

8

Topics learned in later sections

  1. What is a square root?