If what is (i) (ii) (iii) (iv)

Power Play (Exponents) | FIO

Question 9

If $12^2 = 144$ what is

(i) $(1.2)^2$

(ii) $(0.12)^2$

(iii) $(0.012)^2$

(iv) $120^2$

Solution

We will use the given square of 12 and exponent rules to find the other values.

Step 1 — Using the given information

We are given that the square of 12 is 144. This means $12 \times 12 = 144$ . We will use this fact to solve each part.

Step 2 — Calculating $(1.2)^2$

Let us write the decimal number as a fraction. $1.2$ can be written as $\frac{12}{10}$ . Now we need to square this fraction. The rule for squaring a fraction is to square both the numerator and the denominator.

$(1.2)^2 = \left(\frac{12}{10}\right)^2$

$= \frac{12^2}{10^2}$

$= \frac{144}{100}$

$= 1.44$

$\boxed{\mathbf{1.44}}$

Step 3 — Calculating $(0.12)^2$

Let us write $0.12$ as a fraction. $0.12$ can be written as $\frac{12}{100}$ . We will square this fraction using the same rule.

$(0.12)^2 = \left(\frac{12}{100}\right)^2$

$= \frac{12^2}{100^2}$

$= \frac{144}{10000}$

$= 0.0144$

$\boxed{\mathbf{0.0144}}$

Step 4 — Calculating $(0.012)^2$

Let us write $0.012$ as a fraction. $0.012$ can be written as $\frac{12}{1000}$ . We will square this fraction.

$(0.012)^2 = \left(\frac{12}{1000}\right)^2$

$= \frac{12^2}{1000^2}$

$= \frac{144}{1000000}$

$= 0.000144$

$\boxed{\mathbf{0.000144}}$

Step 5 — Calculating $(120)^2$

We can write 120 as a product of 12 and 10. So, $120 = 12 \times 10$ . The rule for squaring a product is to square each factor.

$(120)^2 = (12 \times 10)^2$

$= 12^2 \times 10^2$

$= 144 \times 100$

$= 14400$

$\boxed{\mathbf{14400}}$

Answer

(i) $\mathbf{1.44}$ (ii) $\mathbf{0.0144}$ (iii) $\mathbf{0.000144}$ (iv) $\mathbf{14400}$

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If $12^2 = 144$ what is

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