Find the squares of:

(i) 31, (ii) 72; (iii) 37; (iv) 166.

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Solution

(i) (a + b)² = a² + 2ab + b²

∴31² = (30 + 1)² = 30² + 2 × 30 × 1 + 1²= 900 + 60 + 1 = 961

(ii) (a + b)² = a² + 2ab + b²

∴72² = (70 + 2)² = 4900 + 280 + 4 = 5184

(iii) (a + b)² = a² + 2ab + b²

∴37² = (30 + 7)² = 900 + 420 + 49 = 1369

(iv) (a + b)² = a² + 2ab + b²

∴166² = (160 + 6)² = 25600 + 1920 + 36 = 27556

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Q. Find the squares of the following numbers using column method. Verify the result by finding the square using the usual multiplication:
(i) 25
(ii) 37
(iii) 54
(iv) 71
(v) 96

Find the squares of the following numbers using column method. Verify the result by finding the square using the usual multiplication:
(i) 25 (ii)37
(iii)54 (iv)71
(v)96

Q. Find the squares of the following numbers
(i)

\frac{3}{8}

(ii)

\frac{7}{10}

(iii)

\frac{1}{5}

(iv)

\frac{2}{3}

(v)

\frac{31}{40}

Multiply:
(i) $\sqrt{3} (\sqrt{7} - \sqrt{3})$

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(iii) $(3 \sqrt{2} - \sqrt{3}) (4 \sqrt{3} - \sqrt{2})$

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Find the squares of: (i) 31, (ii) 72; (iii) 37; (iv) 166.

Find the squares of:

(i) 31, (ii) 72; (iii) 37; (iv) 166.