Question

The value of $\sqrt{29\frac{4}{25}}$ is:

• A. 5.6
• B. 5.4
• C. 5.2
• D. 5.5

Answer 1

Answer:

B. 5.4

The value of the given expression is $5\frac{2}{5}$ (or 5.4).

$\sqrt{29\frac{4}{25}}$

1. Convert the mixed fraction into an improper fraction:

* Multiply the whole number by the denominator: $29 \times 25 = 725$

* Add the numerator: $725 + 4 = 729$

* Place it over the denominator: $\frac{729}{25}$

2. Take the square root of both the numerator and denominator:

$\sqrt{\frac{729}{25}} = \frac{\sqrt{729}}{\sqrt{25}}$

3. Calculate the square roots:

* $\sqrt{729} = 27$ (since $27 \times 27 = 729$)

* $\sqrt{25} = 5$ (since $5 \times 5 = 25$)

4. Convert back to a mixed fraction or decimal:

* As an improper fraction: $\frac{27}{5}$

* As a mixed fraction: $5\frac{2}{5}$

* As a decimal: 5.4