Question

How do you simplify $4\sqrt {625} $?

Answer 1

Hint: Here in this question, we have to simplify the given number. The number contains a square root first we have to find the square root of 625 and then we have to multiply to obtain the number to 4. Then after multiplication we obtain the required solution.

Complete step by step solution:
The square is the number times itself. The square is the same as the power of 2. The square root is the opposite of the square. To solve the above question first we have to find the value of $\sqrt {625} $. To solve the square root, we use the division method. So, we have

5	625
5	125
5	25
5	5
	1

The number 625 can be written as $625 = 5 \times 5 \times 5 \times 5$
$ \Rightarrow 625 = {5^2} \times {5^2}$
Therefore, it can be written as
$ \Rightarrow 625 = 25 \times 25$
Therefore, it can be written in the form of square, so we get
$ \Rightarrow 625 = {25^2}$
So, the given question is written as $ \Rightarrow 4\sqrt {{{25}^2}} $
Since the square root and square are inverse. So, we can cancel the square root and square and it is written as
 $ \Rightarrow 4 \times 25$
On the multiplication we get
$ \Rightarrow 100$
Therefore, we have $4\sqrt {625} = 100$
Or we can solve the above question by another method. We apply the square to 4 and shift the number into the square root. So we have
$4\sqrt {625} = \sqrt {16 \times 625} $. Now multiply the both numbers we obtain the answer as $\sqrt {10000} $, now find the square root for 10000 by division method we get

10	10000
10	1000
10	100
10	10
	1

Therefore the 10000 is written as $10000 = 10 \times 10 \times 10 \times 10$
$ \Rightarrow 10000 = {10^2} \times {10^2}$
$ \Rightarrow 10000 = 100 \times 100$
This can be written in the form of squares as $ \Rightarrow 10000 = {100^2}$
Therefore $ \Rightarrow \sqrt {10000} = \sqrt {{{100}^2}} $
Square and square root will cancel and we get
$ \Rightarrow 4\sqrt {625} = 100$
Hence, we have simplified the given number
Therefore $4\sqrt {625} = 100$

Note: When the number is multiplied twice by the number itself then we can say it has a square. The square and square root is inverse of one another. To find the square root of a given number we use the division method. Hence we can simplify the number with the help of a table of multiplication.