Question

find the square root of 289116 by prime factorisation​

Answer 1

Given:

$\sqrt{289116}$

We have to find, the value of $\sqrt{289116}$ is:

Solution:

∴ $\sqrt{289116}$

289116 = 2 × 2 × 3 × 3 × 3 × 2677

∴ $\sqrt{289116}$

= $\sqrt{2 \times 2 \times 3 \times 3 \times 3 \times 2677}$

= 2 × 3 × $\sqrt{3\times 2677}$

= 6$\sqrt{8031}$

∴ The value of $\sqrt{289116}$ = 6$\sqrt{8031}$

Thus, the value of $\sqrt{289116}$ is equal to "6$\sqrt{8031}$".