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Last updated on December 2nd, 2024
The square root of 32 is a value โyโ such that when โyโ is multiplied by itself โ y โคซ y, the result is 32. The number 32 has a unique non-negative square root, called the principal square root.
The square root of 32 is ยฑ5.656854โฆ . Finding the square root is just the inverse of squaring a number and hence, squaring 5.656854โฆ will result in 32. The square root of 32 is written as โ32 in radical form. In exponential form, it is written as (32)1/2
We can find the square root of 32 through various methods. They are:
The prime factorization of 32 is done by dividing 32 by prime numbers and continuing to divide the quotients until they canโt be divided anymore.
After factorizing 20, make pairs out of the factors to get the square roo
If there exist numbers that cannot be made pairs further, we place those numbers with a โradicalโ sign along with the obtained pairs.
So, Prime factorization of 32 = 2 ร 2 ร 2 ร 2 ร 2
But here in case of 32, two pairs of factor 2 can be obtained and a single 2 is remaining
So, it can be expressed as โ32 = 2 ร 2 รโ2 = 4โ2
4โ2 is the simplest radical form of โ32
This is a method used for obtaining the square root for non-perfect squares, mainly. It usually involves the division of the dividend by the divisor, getting a quotient and a remainder too sometimes.
Follow the steps to calculate the square root of 32:
Step 1: Write the number 32, and draw a horizontal bar above the pair of digits from right to left.
Step 2: Now, find the greatest number whose square is less than or equal to 32. Here, it is
5, Because 52=25 < 32.
Step 3: Now divide 32 by 5 (the number we got from Step 2) such that we get 5 as quotient
and then multiply the divisor with the quotient, we get 25
Step 4: Subtract 25 from 32. Add a decimal point after the quotient 5, and bring down two zeroes and place it beside the difference 7 to make it 700.
Step 5: Add 5 to same divisor, 5. We get 10.
Step 6: Now choose a number such that when placed at the end of 10, a 3-digit number will be formed. Multiply that particular number by the resultant number to get a number less than 700. Here, that number is 6.
106ร6=636<700.
Step 7: Subtract 700-636=64. Again, bring down two zeroes and make 64 as 6400. Simultaneously add the unitโs place digit of 106, i.e., 6 with 106. We get here, 112. Apply Step 5 again and again until you reach 0.
We will show two places of precision here, and so, we are left with the remainder, 77500 (refer to the picture), after some iterations and keeping the division till here, at this point
Step 8 : The quotient obtained is the square root. In this case, it is 5.65โฆ.
Approximation or estimation of square root is not the exact square root, but it is an estimate.
Here, through this method, an approximate value of square root is found by guessing.
Follow the steps below:
Step 1: Find the nearest perfect square number to 32. Here, it is 25 and 36.
Step 2: We know that, โ25=5 and โ36=6. This implies that โ32 lies between 5 and 6.
Step 3: Now we need to check โ32 is closer to 5 or 6. Let us consider 5.5 and 6. Since (5.5)2=30.25 and (6)2=36.
Thus, โ32 lies between 5.5 and 6.
Step 4: Again considering precisely, we see that โ32 lies close to (5.5)2=30.25. Find squares of (5.6)2=31.36 and (5.8)2= 33.64.
We can iterate the process and check between the squares of 5.62 and 5.7 and so on.
We observe that โ32=5.65โฆ