Q25 of 50 Page 6

Observe the following pattern


And find the values of each of the following.


(i)


(ii)

R.H.S = [(No. of terms in L.H.S) × (No. + 1) × (2 × No. + 1)]

(i) 12 + 22 + 32 + 42 + …… + 102 = [10 (10 + 1) × (2 × 10 + 1)]


= [2310]


= 385


(ii) 52 + 62 +….. + 122 = 12 + 22 + ….. 122 – (12 + 22 + 33 + 42)


= [12 × (12 + 1) × (2 × 12 + 1)] - [4 ×(4 + 1) × (2 × 4 + 1)]


= 650 – 30


= 620

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21

Find the square root of 11 correct to five decimal places.

 22

The area of a square field is . Calculate the length of the side of the square.

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A PT teacher wants to arrange maximum possible number of 6000 students in a field such that the number of rows is equal to the number of columns. Find the number of rows if 71 were left out after arrangement.

 24

Find the smallest number by which the given number must be multiplied so that the product is a perfect square:

(i) 23805


(ii) 12150


(iii) 7688