Square Root of 49/16
2026-02-28 12:06 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-49-by-16

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Last updated on December 15, 2025

If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 49/16.

What is the Square Root of 49/16?

The square root is the inverse of the square of the number.

49/16 is a rational number.

The square root of 49/16 can be expressed in both radical and exponential form.

In radical form, it is expressed as √(49/16), whereas in exponential form it is (49/16)^(1/2). Simplifying the square root, we get √49/√16 = 7/4, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.

Finding the Square Root of 49/16

Square Root of 49/16 by Simplification Method

The simplification method is straightforward for numbers whose numerator and denominator are perfect squares.

Here's how we simplify the square root of 49/16:

Step 1: Identify the perfect squares in the numerator and denominator. The numerator 49 is a perfect square, i.e., 72, and the denominator 16 is a perfect square, i.e., 42.

Step 2: Express the square root of the fraction as the square root of the numerator over the square root of the denominator. √(49/16) = √49/√16

Step 3: Simplify the square roots. √49 = 7 and √16 = 4, so √(49/16) = 7/4.

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Applications of the Square Root of 49/16

The square root of 49/16, being 7/4, is often used in various practical applications where ratios are involved.

For instance, it can be used in fields like engineering, physics, and finance to simplify complex fractions and aid in calculations involving proportions and ratios.

Common Mistakes in Finding Square Roots

When working with square roots, particularly those involving fractions, there are common mistakes to be aware of:

Mistaking Simplification Steps

One common mistake is overlooking the need to simplify both the numerator and denominator separately before taking the square root.

For instance, not recognizing that √(49/16) should be simplified to √49/√16 before finding the square root.

Common Mistakes and How to Avoid Them in the Square Root of 49/16

Students may make errors while finding the square root of fractions, such as misapplying simplification steps or overlooking the need to express the square root in its simplest form.

Here are some common mistakes and how to avoid them.

Problem 1

Can you help Max find the area of a square box if its side length is given as √(49/16)?

Okay, lets begin

The area of the square is 49/16 square units.

Explanation

The area of the square = side2.

The side length is given as √(49/16).

Area of the square = (7/4)2 = 49/16.

Therefore, the area of the square box is 49/16 square units.

Well explained 👍

Problem 2

A square-shaped plot measuring 49/16 square meters is built; if each of the sides is √(49/16), what will be the square meters of half of the plot?

Okay, lets begin

The plot measures 49/32 square meters.

Explanation

We can divide the given area by 2 since the plot is square-shaped.

Dividing 49/16 by 2 = 49/32.

So half of the plot measures 49/32 square meters.

Well explained 👍

Problem 3

Calculate √(49/16) x 8.

Okay, lets begin

14

Explanation

First, find the square root of 49/16, which is 7/4.

Then, multiply 7/4 by 8.

(7/4) x 8 = 56/4 = 14.

Well explained 👍

Problem 4

What will be the square root of (25/16 + 24/16)?

Okay, lets begin

The square root is 3.

Explanation

To find the square root, first sum the fractions:

(25/16 + 24/16) = 49/16.

Then, √(49/16) = 7/4 = 1.75.

Therefore, the square root of (25/16 + 24/16) is 3.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √(49/16) units and the width ‘w’ is 3 units.

Okay, lets begin

The perimeter of the rectangle is 11.5 units.

Explanation

Perimeter of the rectangle = 2 × (length + width).

Perimeter = 2 × (7/4 + 3)

= 2 × (1.75 + 3)

= 2 × 4.75

= 9.5 units.

Well explained 👍

FAQ on Square Root of 49/16

1.What is √(49/16) in its simplest form?

The prime factorization of 49 and 16 results in perfect squares, so the simplest form of √(49/16) = √49/√16 = 7/4.

2.What are the factors of 49/16?

Factors of 49/16 are derived from the factors of 49 and 16 individually. 49 has factors 1, 7, 49, and 16 has factors 1, 2, 4, 8, 16.

3.Calculate the square of 49/16.

We get the square of 49/16 by multiplying the number by itself, which is (49/16) x (49/16) = 2401/256.

4.Is 49/16 a rational number?

Yes, 49/16 is a rational number as it can be expressed as the ratio of two integers, where the denominator is not zero.

5.What is the decimal representation of √(49/16)?

Important Glossaries for the Square Root of 49/16

  • Square root: A square root is the inverse of squaring a number. For example, if 42 = 16, then the square root of 16 is √16 = 4.
     
  • Rational number: A rational number is a number that can be expressed as the quotient of two integers, with the denominator not equal to zero. 49/16 is rational.
  • Perfect square: A perfect square is a number that is the square of an integer. Both 49 and 16 are perfect squares.
  • Fraction: A fraction is a numerical quantity that is not a whole number, represented by two numbers separated by a slash, like 49/16.
  • Decimal: A decimal number includes a whole number and a fractional part separated by a decimal point, such as 1.75.

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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

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