Sandra plan on building a squarepool in her backyard. She desires the pool to have actually an area of169 square feet. She is make the efforts to calculation the next of the pool.To calculate the side of a square-shaped object, we have to uncover the square root of the offered area.Square root of 169 is the number which once multipliedby itself provides the product as 169. In this lesson, we will calculate the square root of 169 by long department method and also solve a couple of interesting problems.

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Square source of 169: 13Square of 169: 28,561
1.What Is the Square root of 169?
2.IsSquare source of 169 rational or Irrational?
3.How to discover the Square root of 169?
4.FAQs ~ above Square root of 169
5.Important notes on Square source of 169
6.Challenging Questions

169 = a ×a = a2Thus, a =√169 = √(13 ×13)13 × 13 = 169 or -13 ×-13 = 169Thus the square root of 169 is +13 or -13.This shows that 169 is a perfect square.

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13 and also -13 can be expressed as 13/1 and also -13/1Both numbers have the right to be represented in the type of a reasonable number.Hence, the square root of 169 is a rational number.

The square root of 169 deserve to be calculatedusing different methodssuch together prime administer or the long department method or the repeated subtraction method.

Square source of 169 by recurring Subtraction Method

Start from 169 and also keep subtracting the successive odd numbers till we obtain zero. The total numbers we subtract is the square root of 169.

169 - 1 = 168168 - 3 = 165165 - 5 = 160160 - 7 = 153153 - 9 = 144144 -11 = 133133 -13 = 120120 -15 = 105105 - 17 =8888 - 19 = 6969 - 21 = 4848 - 23 =2525 - 25 = 0

Thus beginning from 169, we have subtracted 13 time to obtain 0. Thus, the square root of 169 is 13.


Write 169. Take it the number in pairs from the right. 69 is preferred as a pair and one stands alone.Now division 1 through a number such the number× numbergives 1 or a number lesser than that.Obtain 1 together the quotient and also 0 together the remainder.Bring down 69for division.Multiply the quotient derived in the previous action with 2. Currently 1× 2 = 2;20 is written in the divisor's place.Find a number which can be included to 20 and this sum deserve to be multiplied by that numbersuch that the product is 69 or lesser 보다 that.We uncover that 3 is the number. 20 + 3 = 23 and also 23 ×3 gives 69.Now our quotient is 13 and also the remainder is 0.

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Explore Square roots using illustrations and interactive examples


The square source of 169is expressed together √169 in the radical type and as 169½ in exponential form.The square source of a number is both negative and positive for the very same numerical value, i.e., the square source of 169 is +13 or -13.The square root of only perfect squares can be calculated quickly using the element factorization an approach or repeated subtraction method.169 is a perfect square.
Thomas is replacingthe shutters on a square windowof area 16.9 square inches. Exactly how high will certainly the shutters be?In a class, every of the students added as countless dollars together the totalnumber the students. If the full collection to be $16900, how countless students were there in the class?

Example 1:A new squareplayground is being developed on an area the 676square yards. The ground will certainly be divided into 4 equal sections. What will be the size of every side the thesection?

Solution:

The complete area of the park= 676 square yards

Total sections of the park = 4

Area the each section of the park = full area of the park ÷Number of sections

676 ÷4 = 169 square yards

We know thateach next of the square = √169

Thus, the length of every side the the section=13yards


Example 2 :Shane has actually a square ceiling that has actually an area that 256 square inches.The blanket has an embroidered border that a particular width. The internal area the the blanket is 169 square inches. Can you calculation the broad of the embroidery of the blanket?