Last updated on May 26th, 2025
If a number is multiplied by itself, the result is a square. The inverse of squaring a number is finding its square root. The square root is used in fields such as architecture, finance, and engineering. Here, we will discuss the square root of 962.
The square root is the inverse operation of squaring a number. The number 962 is not a perfect square. The square root of 962 is expressed in both radical and exponential form. In radical form, it is expressed as √962, whereas in exponential form it is written as 962(1/2). The square root of 962 is approximately 31.014, which is an irrational number because it cannot be expressed as a fraction p/q, where p and q are integers and q ≠ 0.
The prime factorization method is typically used for perfect square numbers. However, for non-perfect squares like 962, the long division method and approximation method are more suitable. Let us explore these methods: -
The long division method is particularly useful for finding the square root of non-perfect square numbers. Here is how you can find the square root of 962 using the long division method, step by step:
Step 1: Begin by pairing the digits of 962 from right to left, which gives us 62 and 9.
Step 2: Find the largest number whose square is less than or equal to 9. That number is 3 because 3 × 3 = 9. Subtract 9 from 9, leaving a remainder of 0.
Step 3: Bring down the next pair, which is 62, making the new dividend 62.
Step 4: Double the divisor (3) to get 6, which becomes the new divisor prefix. Now, determine a digit n such that 6n × n is less than or equal to 62.
Step 5: The largest n satisfying this condition is 1, since 61 × 1 = 61. Subtract 61 from 62 to get a remainder of 1.
Step 6: Add a decimal point to the quotient and bring down two zeros to make the new dividend 100.
Step 7: Double the current quotient (31) to get 62. Find a digit n such that 62n × n is less than or equal to 100.
Step 8: The largest n is 1, since 621 × 1 = 621. Subtract 621 from 1000 to get a remainder of 379.
Step 9: Continue this process until you achieve the desired accuracy. The square root of 962 is approximately 31.014.
The approximation method provides a quick and easy way to estimate the square root of a number. Here's how to find the square root of 962 using this method:
Step 1: Identify the perfect squares nearest to 962. The perfect squares are 961 (31²) and 1024 (32²). Thus, √962 is between 31 and 32.
Step 2: Use the formula: (Given number - smaller perfect square) / (Larger perfect square - smaller perfect square). Using this formula: (962 - 961) / (1024 - 961) = 1/63 ≈ 0.0159.
Adding this to 31 gives approximately 31.0159, so √962 ≈ 31.014.
Students often make mistakes when finding square roots, such as forgetting about negative roots or misapplying methods. Here are some common mistakes and how to avoid them.
Can you help Max find the area of a square box if its side length is given as √962?
The area of the square is approximately 924.868 square units.
The area of a square is calculated as side².
Given the side length as √962, the area = (√962)² = 962.
Therefore, the area of the square box is approximately 924.868 square units when rounded.
A square-shaped garden measuring 962 square feet is built. If each side is √962, what will be the square feet of half of the garden?
481 square feet
To find half the area of the square, divide the total area by 2.
So, 962 ÷ 2 = 481.
Therefore, half of the garden measures 481 square feet.
Calculate √962 × 5.
Approximately 155.07
First, find the square root of 962, which is approximately 31.014.
Then multiply 31.014 by 5.
So, 31.014 × 5 ≈ 155.07.
What will be the square root of (962 - 2)?
The square root is approximately 31.
First, find the difference: 962 - 2 = 960. Then find the square root of 960, which is approximately 31.
Find the perimeter of a rectangle if its length ‘l’ is √962 units and the width ‘w’ is 38 units.
The perimeter of the rectangle is approximately 138.028 units.
Perimeter of a rectangle = 2 × (length + width).
Given length = √962 and width = 38:
Perimeter = 2 × (31.014 + 38)
= 2 × 69.014 = 138.028 units.
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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