Question

Find the square root of 10 151/225

Answer 1

The square root of $10\dfrac{151}{225}$ is $3\dfrac{4}{15}$.

Step-by-step explanation:

Step 1. Let us express the given mixed fraction as an improper fraction first.

$\quad 10\dfrac{151}{225}$

$=10+\dfrac{151}{225}$

$=\dfrac{10\times 225}{225}+\dfrac{151}{225}$

$=\dfrac{10\times 225+151}{225}$

$=\dfrac{2250+151}{225}$

$=\dfrac{2401}{225}$

Step 2. Now we prime factorize the numerator and denominator to check whether they are perfect squares.

Here,

• $2401=7\times 7\times 7\times 7=7^{2}\times 7^{2}=(7\times 7)^{2}=49^{2}$

• $225=3\times 3\times 5\times 5=3^{2}\times 5^{2}=(3\times 5)^{2}=15^{2}$

Clearly, $2401$ and $225$ are perfect squares.

Step 3. We find the required square root.

Now, $\sqrt{10\dfrac{151}{225}}$

$=\sqrt{\dfrac{2401}{225}}$

$=\dfrac{\sqrt{2401}}{\sqrt{225}}$

$=\dfrac{\sqrt{49^{2}}}{\sqrt{15^{2}}}$

$=\dfrac{49}{15}$

$=3\dfrac{4}{15}$

Answer 2

Answer:

Step-by-step explanation: