Square Root Using Prime Factorization
Square Root Using Prime Factorization
Square Root: The square root of a number a is that number which when multiplied by itself gives 'a' as the product.
Property: Negative numbers have no square root in the system of rational numbers.
Explanation:
We have, and so on.
Also,
and so on. This means that the square of a number whether positive or negative is always positive. Consequently, negative numbers are not perfect squares. Hence, negative have no square roots.
Square Root Of a Perfect Square By Prime Factorization
In order to find the square root of a perfect square by prime factorization, we follow the following steps.
STEP I Obtain the given number.
STEP II Resolve the given number into prime factors by successive division.
STEP III Make pairs of prime factors such that both the factors in each pair are equal. Since the number is a perfect square, you will be able to make an exact number of pairs of prime factors.
STEP IV Take one factor from each pair.
STEP V Find the product of factors obtained in step IV.
STEP VI The product obtained in step V is the required square root.
The following examples will illustrate the above procedure.
Illustration 1: Find the square root of 7744 by prime factorization.
By what numbers should each of the following be divided to get a perfect square each case? Also, find the number whose square is the new number : 3174 | |||
| Right Option : B | |||
| View Explanation | |||
Find the smallest number by which the given number 7688 must be multiplied so that the product is a perfect square. | |||
| Right Option : B | |||
| View Explanation | |||
Find the smallest number by which the given number must be multiplied so that the product is a perfect square: 12150 | |||
| Right Option : C | |||
| View Explanation | |||
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