find the square root of 60025
Answers
Answer:
How do I find 60025−−−−−√ without using a calculator?
Square of a number ending in 5 say N5 always ends in 25. And the rest of the digits to the left of 25 are obtained by Nx(N+1) e.g. 35^2=[3x4]25=1225 using N=3
For sq rt of [600]25, all you need is to find N such that Nx(N+1)=600. Easy to see 24x25=600
Answer must be [24]5
There is an arithmetic procedure to calculate square roots, similar to long division.
I’ll use x for our root-so-far. We will find the digits of x starting from the largest value.
First, split 60025 into groups of 2 digits (starting from the right). We get: 6 00 25.
Let the first digit of x be the largest such that the digit squared does not exceed 6 (our first group of digits). This is 2. So x starts with a 2.
Now, subtract x2 from 6 (which gives us 2) and add the next group of digits, resulting in 200. Now we find the next digit of the root, which is y such that y2+20xy does not exceed 200. This y is 4. So our new x becomes 24. The remainder is 200−(16+160)=24 . We add the next group of 2 digits to the remainder and get 2425 . We need to find the largest digit y such that y2+20xy=y2+480y does not exceed 2425 . We have y=5 , our square root becomes 245 and the remainder is 0 , indicating that 60025 is indeed a perfect square. Otherwise, we could continue the process, getting one decimal at a time, until we are satisfied with the precision.
Step-by-step explanation:
l hope it will help u ✌️☺️✌️
Square root of 60025 is 250