What is the Square Root of 49?

S1-SA1-1221

Grade Level:

Class 4

Maths, Computing, AI

Definition

What is it?

The square root of a number is another number which, when multiplied by itself, gives the original number. So, the square root of 49 is the number that you multiply by itself to get 49.

Simple Example

Quick Example

Imagine you have a square cricket field, and its area is 49 square meters. To find the length of one side of this square field, you would calculate the square root of 49. The side length would be 7 meters, because 7 multiplied by 7 equals 49.

Worked Example

Step-by-Step

Let's find the square root of 49:
1. We are looking for a number that, when multiplied by itself, equals 49.
2. Let's try some whole numbers:
3. Is 5 x 5 = 25? No, too small.
4. Is 6 x 6 = 36? No, still too small.
5. Is 7 x 7 = 49? Yes, this is correct!
6. So, the square root of 49 is 7.
Answer: The square root of 49 is 7.

Why It Matters

Understanding square roots is key for many fields. In computing, it helps with graphics and game development. For AI, it's used in calculations for machine learning models. Engineers use it to design buildings and bridges, and data scientists use it to analyze large datasets.

Common Mistakes

MISTAKE: Confusing square root with division by 2 (e.g., thinking sqrt(49) is 49/2). | CORRECTION: Remember, square root means finding a number that multiplies by ITSELF to get the original number, not dividing by 2.

MISTAKE: Forgetting that a number can have both a positive and negative square root (e.g., only giving 7 as the answer for sqrt(49)). | CORRECTION: While 7 x 7 = 49, also remember that (-7) x (-7) = 49. So, the square roots are +7 and -7.

MISTAKE: Trying to find a whole number square root for numbers that don't have one (e.g., thinking sqrt(50) is a whole number). | CORRECTION: Not all numbers have a perfect whole number square root. For numbers like 50, the square root will be a decimal.

Practice Questions

Try It Yourself

QUESTION: What is the square root of 25? | ANSWER: 5

QUESTION: If a square photo frame has an area of 81 square centimeters, what is the length of one of its sides? | ANSWER: 9 centimeters

QUESTION: Find the value of 3 times the square root of 100. | ANSWER: 30

MCQ

Quick Quiz

Which of these numbers, when multiplied by itself, gives 64?

The Correct Answer Is:

The correct answer is 8 because 8 multiplied by 8 equals 64. Options A, B, and D give 36, 49, and 81 respectively when multiplied by themselves.

Real World Connection

In the Real World

Imagine you're designing a square garden for your school, and you know its area. To buy the right amount of fencing, you need to find the length of one side. This is exactly where finding the square root helps! Similarly, engineers at ISRO use square roots in calculations for satellite orbits and rocket trajectories.

Key Vocabulary

Key Terms

SQUARE ROOT: A number that, when multiplied by itself, gives the original number | SQUARE: The result of multiplying a number by itself | AREA: The amount of space a flat shape covers | PERFECT SQUARE: A number whose square root is a whole number

What's Next

What to Learn Next

Great job understanding square roots! Next, you can explore 'Cube Roots', which is a similar concept but involves multiplying a number by itself three times. This will help you understand more complex mathematical operations.