MCQ test, Set 2

Answer: (C) $41^2$

$41$ is multiplied by itself $2$ times.

$\therefore 41 \times 41 = 41^2$

Answer: (B) $361$

$361 = 19 \times 19 = 19^2$

The other numbers are not in the table of squares.

Answer: (D) $676$

In the table, $24^2$ and $26^2$ differ by $100$, $23^2$ and $27^2$ by $200$, $22^2$ and $28^2$ by $300$, $21^2$ and $29^2$ by $400$.

$26^2 = 576 + 100 = 676$

Answer: (C) $900$

$30^2 = 30 \times 30$

$3 \times 3 = 9$, then write two zeros: $900$

Answer: (A) $12$

Rule: multiply the number before $5$ by the next number, then write $25$.

$3 \times 4 = 12$, so $35^2 = 1225$

Answer: (B) $124$

$a^2 = b \Rightarrow \sqrt{b} = a$

$124^2 = 15376 \Rightarrow \sqrt{15376} = 124$

(The square root is not half the number.)

Answer: (A) $14$

$14^2 = 14 \times 14 = 196$

$\therefore \sqrt{196} = 14$

Answer: (D) $289$

$\sqrt{b} = a \Rightarrow b = a^2$

$17^2 = 17 \times 17 = 289$

Answer: (A) $18$

Take one factor from each pair: $2 \times 3 \times 3 = 18$

Answer: (C) $22$

$\sqrt{2 \times 2 \times 11 \times 11} = \sqrt{(2 \times 2) \times (11 \times 11)}$

$= 2 \times 11 = 22$

Answer: (B) $57$

Pairs: $\overline{32}\;\overline{49}$.

$5 \times 5 = 25 \le 32$: first digit $5$, and $32 - 25 = 7$

Bring down $49$: we get $749$. New divisor: $5 \times 2 = 10$; $107 \times 7 = 749$ ($108 \times 8 = 864$ is too big); $749 - 749 = 0$

Remainder $0$. $\therefore \sqrt{3249} = 57$

Answer: (A) $16$

Double the root found so far: $8 \times 2 = 16$

Then $165 \times 5 = 825$ ($166 \times 6 = 996$ is too big), so $\sqrt{7225} = 85$

Answer: (C) $3$

Pairs from the right: $\overline{20}\;\overline{43}\;\overline{04}$, that is $3$ groups.

One digit of the root for each group: $\sqrt{204304} = 452$

Answer: (D) $6$

$\sqrt{2} \times \sqrt{18} = \sqrt{2 \times 18} = \sqrt{36} = 6$

Answer: (A) $21$

$(\sqrt{a})^2 = \sqrt{a} \times \sqrt{a} = a$

$\therefore (\sqrt{21})^2 = 21$

Answer: (D) $3$

$\displaystyle \frac{\sqrt{63}}{\sqrt{7}} = \sqrt{\frac{63}{7}} = \sqrt{9} = 3$

Answer: (D) $\sqrt{26}$

$\displaystyle \frac{26}{\sqrt{26}} = \frac{\sqrt{26} \times \sqrt{26}}{\sqrt{26}} = \sqrt{26}$

Answer: (B) $11$

$\sqrt{16} + \sqrt{49} = 4 + 7 = 11$

$\sqrt{a} + \sqrt{b} \ne \sqrt{a + b}$, so do not add first.

Answer: (A) $2$

$\sqrt{100} - \sqrt{64} = 10 - 8 = 2$

$\sqrt{a} - \sqrt{b} \ne \sqrt{a - b}$, so do not subtract first.

Answer: (C) $25$

$\sqrt{15^2 + 20^2} = \sqrt{225 + 400} = \sqrt{625} = 25$

$\sqrt{a^2 + b^2} \ne a + b$

Answer: (B) $13$

$\sqrt{(a + b)^2} = a + b$ when $a + b > 0$

$\sqrt{(6 + 7)^2} = \sqrt{13^2} = 13$

Answer: (A) $0.06$

$\displaystyle \sqrt{0.0036} = \sqrt{\frac{36}{10000}}$

$\displaystyle = \frac{\sqrt{36}}{\sqrt{10000}}$

$\displaystyle = \frac{6}{100}$

$= 0.06$

Answer: (B) $0.007$

$\displaystyle \sqrt{0.000049} = \sqrt{\frac{49}{1000000}}$

$\displaystyle = \frac{\sqrt{49}}{\sqrt{1000000}}$

$\displaystyle = \frac{7}{1000}$

$= 0.007$

Answer: (C) $1.2$

$\displaystyle \sqrt{1.44} = \sqrt{\frac{144}{100}} = \frac{\sqrt{144}}{\sqrt{100}} = \frac{12}{10} = 1.2$

Answer: (D) $1.69$

$\displaystyle 1.3 = \frac{13}{10}$

$\displaystyle \left(\frac{13}{10}\right)^2 = \frac{169}{100} = 1.69$

Check: $\displaystyle \sqrt{1.69} = \frac{\sqrt{169}}{\sqrt{100}} = 1.3$