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# How do you simplify 4 square roots of 125?

Last updated date: 02nd Aug 2024
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Hint: In order to solve this question, we are required to simplify the given number consisting of a square root. Thus, we will express the given square root number as a product of its factors using the prime factorization method. Then simplifying the square root of 125 and multiplying it by 4, we will get the required answer.

In order to simplify $4\sqrt {125}$
First, we have to find the square root of 125 using the prime factorization method.
Therefore, prime factorization of 125 is.
We can see that 125 is an odd number and 2 and 3 are not a factor of 125.
So, we will divide 125 by the least prime number 5. Therefore, we get
$125 \div 5 = 25$
Dividing 125 by 5, we get
$25 \div 5 = 5$
As we have obtained the quotient as a prime number, so we will not divide the number further.
Hence, 125 can be written as:
$125 = 5 \times 5 \times 5$
But, we will take out 1 factor from the pair of common factors in order to find the square root.
Hence, taking square root on both sides, we get,
$\sqrt {125} = 5\sqrt 5$
Therefore, we can write:
$4\sqrt {125} = 4 \times 5\sqrt 5$
Multiplying the terms, we get
$\Rightarrow 4\sqrt {125} = 20\sqrt 5$

Hence, 4 square roots of 125 can be simplified as 20 square roots of 5.
Thus, this is the required answer.

Note: We know that prime factors are those factors that are greater than 1 and have only two factors, i.e. factor 1 and the prime number itself. In order to express the given number as a product of its prime factors, we are required to do the prime factorization of the given number. Factorization is a method of writing an original number as the product of its various factors. Hence, prime factorization is a method in which we write the original number as the product of various prime numbers.