What are those mysterious square roots that often confuse students and complicate their lives? The truth is that to understand them, we need to grasp the concept of the inverse operation.

What is a square root?

When we solve an exercise like 5=252 5=25^2 , it's clear that 5 5 times 5 5 (that is, multiplying the number by itself) results in 25 25 . This is the concept of a power, or to be more precise, a square power, which to apply, we must multiply the figure or the number by itself.

The concept of "square root" refers to the inverse operation of squaring numbers.

That is, if we have X2=25X^2=25 and we want to find the value of XX, what we need to do is perform an identical operation on both sides of the equation.

A - The concept of square root refers to the inverse operation of squaring numbers

This operation is the square root.

So, we have: X2=25\sqrt{X^2} = \sqrt{25} and the result is X=5 X=5 .

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 Roots

Examples with solutions for Square Roots

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. Square Root of a Negative Number