# Calculate sqrt(7225) without using a calculator.

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sqrt(7225)

first ley us try and factor:

We notice that 7225 is dividable by 5:

==> 7225 = 5*1445

Also 1445 is divisable by 5:

==> 7225 = 5*5*289

Now we know that 289 = 17*17

==> 7225 = 5*5*17*17

==> sqrt7225 = sqrt(5*5*17*17)

= 5*17 = 85

==> sqrt(2775) = 85

We can calculate the square root (sqrt) of a number by factorising it and then finding square roots of the factors.

For example if:

x = (a^2)*(b^2) = (a*b)^2

Then:

sqrt(x) = a*b

Taking the given number (7225) we see that last two digits of this number are 25. Therefore it is divisible by 25. Thus dividing 7225 by 25 we get:

7225 = 25*289

= (5^2)*(17^2)

Therefore:

sqrt(7225) = 5*17 = 85

Answer:

sqrt(7225) = 85

To find the square root of 7225.

We know that (y+x)^2 = y^2+2yx+x^2.

Put y =5 and x =10x

7225 = 5^2 +2*5*(x*10)+(10x)^2

7225-5^2 = 100x+100x^2.

7200 = 100x+ 100x^2. Divide by 100.

72 = x+x^2

x^2+x-72 = 0

(x+9)(x-8) = 0

x+9 =0 Or x-8 = 0

x=-9 Or x= 8.

x= 8 is practical.

So the sqrt 7225 = 5+10x = 5+8*10 = 85.

We can express 7225 as the product of its prime factors as:

7225=1445*5=289*5*5=17*17*5*5

To find the square root of 7225 eliminate one term of each of the prime factors that exist as a pair. Here we have a pair of 17 and a pair of 5. Eliminate one from each. Therefore we are left with 17*5=85.

Therefore the square root of 7225 is 85.

This can be verified by finding the square of 85 which is 7225.