Find the square root of:

(3) 3025

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Solution

Prime factorisation of 3025:

$\begin{matrix} 5 & 3025 \\ 5 & 605 \\ 11 & 121 \\ 11 & 11 \\ 1 \end{matrix}$

= 5 × 5 × 11 × 11
= (5 × 11)²

∴ Square root of 3025 = 5 × 11 = 55

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Now compute the square root of these by factorization.

(i) 3025

(ii) 2304

(iii) 9604

(iv) 6561

Find the square root of:

$(i) \frac{441}{961}$ $(i i) \frac{324}{841}$ $(i i i) 4 \frac{29}{49}$ $(i v) 2 \frac{14}{25}$ $(v) 2 \frac{137}{196}$

$(v i) 23 \frac{26}{121}$ $(v i i) 25 \frac{544}{729}$ $(v i i i) 75 \frac{46}{49}$ $(i x) 3 \frac{942}{2209}$ $(x) 3 \frac{334}{3025}$

$(x i) 21 \frac{2797}{3364}$ $(x i i) 38 \frac{11}{25}$ $(x i i i) 23 \frac{394}{729}$ $(x i v) 21 \frac{51}{169}$ $(x v) 10 \frac{151}{169}$

1^{3} + 2^{3} + . . . . . + m^{3} = 3025

Find the value of a in 3 - square root 5 / 3 + 2 square root 5 = a square root 5 - 19/11

3 - 4 i

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