113 has only 2 factors, 1 and also the number chin (113). Hence, 113is a prime number. On acquisition square source of 113, we have the right to see that√113 can not it is in simplified any type of further. Thus,113 is an irrational number.In this mini-lesson us will find out to uncover square root of 113by long division method together with solved examples. Let us see what the square root of 113is.

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Square root of 113:113 = 10.630Square of 113: 1132 = 12,769

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Thenumber whose square offers 113, is thesquare rootof 113. As there room nointegers whose square will give the worth 113. Hence,113 is offered as,

113 = 10.630

On squaring 10.630, we obtain (10.630)2= 112.9969.. I beg your pardon is close come 113 once it is rounded come its nearest value.

Arational numbereither hasterminating or non-terminating and also hasa repeatingpattern in that decimal part. We have the right to seethat113= 10.63014581273465...This is non-terminating and the decimal part has no repeating pattern.Hence,113is one irrational number.

How to uncover the Square root of 113?

There are differentmethods to discover the square source of any kind of number. Click hereto know much more about the various methods.

Simplified Radical type of Square root of 113

113 isa prime number hence, it has actually only two components 1 and also 113. Hence, the streamlined radical type of 113 is 113.

Square root of 113by Long department Method

The square source of 113can be uncovered using the long department as follows.

Step 1: Pair the digits of 113 starting with a number at one's place. Put a horizontalbar come indicatepairing.Step 2:Now wefind a number i m sorry on multiplicationwithitself provides a product of less than or equal to 1. Together we understand 1× 1= 1 = 1.Step 3:Now, we have to bring down 13 and multiply the quotient through 2. Thisgive us 2. Hence, 2is the starting digit that thenew divisor.Step 4: 0isplaced atone's location of brand-new divisor because when 20 is multiply by 0we get 0. The acquired answer currently is 13and we lug down 00.Step 5: The quotient now becomes 10and itis multiplied by 2. Thisgives 20, which climate would come to be the beginning digit the the brand-new divisor.Step 6: 6is inserted at one's place of brand-new divisor because on multiply 206 by 6we acquire 1236. The price now acquired is64 and also we bring 00 down.Step 7: currently the quotient is 106when multiply by2 provides 212, which will certainly bethe starting digit of the brand-new divisor.Step 8: 3is inserted at one's location of the divisor due to the fact that on multiply 2123by 3we will acquire 6369. The answer obtained is 31 and we carry 00 down.Step 9: currently the quotient is 1063 once multiplied by 2gives 2126, which will certainly bethe starting digit that the brand-new divisor.Step 10: 0is inserted at one's location of the divisor because on multiply 21260by 0,we will obtain 0. The answer obtained is 31 and we carry 00 down.


So far we have got 113 = 10.630. On repeating this procedure further, us get,113= 10.63014581273465...

Explore Square roots making use of illustrations and interactive examples

Important Notes:

113lies between 100 and also 121. Shortly taking the square source on both the sides, we get113 lies in between 100 and121 i.e., 113 lies in between 10and 11.The square source of 113 is irrational. 113is no a perfect square which provides it difficult to simplify113 any type of further.

Can the square source of 113 it is in simplified?

As 113 is no a perfect square. Hence, it cannot be streamlined further.

What is the square root of 113rounded to its nearest tenth?

As, 113 = 10.630. On rounding square root of 113 to its nearest tenth we get, 10.6.

Does 113 have actually a square root?

Yes, 113 has a square root yet it is no a whole number.

What is the value of square root of 113?

As 113 is not a perfect square, that square root is no a totality number. 113= 10.63014581273465(approx)

Is the square source of 113 reasonable or irrational?

The square source of 113is irrational.

Is square root of 113a real number?

Yes, the square source of 113is a real number.

Think Tank:

What is the value of(-113) ?Is the worth of(-113) exact same as -113?

Square root of 113 fixed Examples

Example 1: Is it possible to right a carpet that 8 feet length in a room of area 113 square feet?


Let us assume that the size of the room is xfeet. Climate the area that the room's floor is x2square feet. Through the provided information:

x2= 113x = √113= 10.6feet (approx)

The size of the room is 10.6feet. Together the length of carpet is lesser than the length of room, the is possible to fit the ina room the area 113 square feet.

See more: How Many Feet Is 9 Yards To Feet, Convert 9 Yards To Feet

Example 2: What is the difference between the radiiof one having areas of one 113π square inchesand 100π square inches?


For detect radius the circle having area113π we usage the formula, area = πr2= 113πr2 = 113√r2=113By calculating the square source of 113is 10.6 inches.For finding radius of circle having area100π we use the formula, area = πr2= 100πr2 = 100√r2=100By calculating the square source of 100 is 10 inches.Hence, the difference in between the radii of one having locations of circles113π square inchesand 100π square customs is (10.6 - 10) inches = 0.4 inches.