Question

Find the square of 35 by using column method.verify the result by finding the square using the prime factorisation method

Answer 1

Answer:

1225

Step-by-step explanation:

Consider a = 3 and b = 5

From the formula, let us take a^2 as column 1, 2*a*b as column 2 and b^2 as column 3.

$(35)^2 \\ \\ a = 3,\:\: b = 5\\ \\\begin{tabular}{ c | c | c }CI & CII & CIII \\ \cline{1-3}9 & 30 & 2\underline5 \\ +3& +\underline2 &\\ \cline{1 - 3}\underline{12}& 3\underline2&\end{tabular}$

Column 1 = a^2 = 3*3 =9

Column 2 = 2*a*b = 2*3*5= 30

Column 3 = b*b = 5*5 = 25

Underline the unit digit of b^2, add its tens digit to column 2 value.

b^2 = 25

2ab = 30+2=32

Underline the unit digit of 2ab,add its tens and other digit values to a^2.

2ab =32

a^2 = 12

So a^2 will be 12

Write final underlined a^2,2ab,b^2 together in a sequence.

1225

∴ Square of 35 is 1225