find the square of the following numbers
(1) 24
(2) 42
(3) 66
give it's solution step by step in image form
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Answers
hey there!!
Answer:
1) 4.89897948557
2) 6.48074069841
3) 8.12403840464
Step-by-step explanation:
1) 24
The square root of 24 by long division method consists of the following steps:
Step 1: Starting from the left, first pair 24 and place a bar over the digits. We also pair the 0s in decimals in pairs of 2 from left to right.
Step 2: Find a number that, when multiplied to itself, gives the product less than or equal to 24. The number 4 fits here. Putting the divisor as 4, we get the quotient as 4 and the remainder as 8.
Step 3: Drag a pair of 0’s down and fill it next to 8 to make the dividend 800.
Step 4: Double the divisor 4, and enter 8 below with a blank digit on its right. Guess the largest possible digit(X) to fill in the blank and the quotient for which the product of 8X and X results in a value less than or equal to 800. Divide and write the remainder.
Step 5: Repeat this process to get the decimal places you want.
b) 42
Find two consecutive perfect squares between which the number 42 lies. The two numbers are 36 (62) and 49 (72).
So, the whole number part of the square root of 42 will be 6.
Now, for the decimal part we will use the formula:
(Given number - Smaller perfect square) / (Greater perfect square - smaller perfect square)
= (42 - 36)/(49 - 36) = 6/13 = 0.461
So, the estimated square root of 42 by the approximation method is 6.461.
c) 66
We will find two consecutive perfect squares such that 66 lies between them. The two perfect squares are 64 (82) and 81 (92).
So, the whole number part of the square root of 66 will be 8.
Now, for the decimal part, we will use the formula:
(Given number - Smaller perfect square) / (Greater perfect square - Smaller perfect square)
= (66 - 64)/(81 - 64) = 2/17 = 0.117
Hence, the square root of 66 by approximation method is 8.117
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