Question

Write square root of 5 x square root 10 in the form of b square root of 2 where b is an integer

simplify fully square root of 27 x square root of 75

Answer 1

`\textbf{a)}\\\\~~~\sqrt 5 * √(10)\\\\=√(5) * √(5 * 2)\\\\=√(5) * \sqrt 5 * \sqrt 2\\\\=\left(\sqrt 5 \right)^2 * \sqrt 2\\\\=5\sqrt 2\\\\\text{It is now in a form of} ~ b\sqrt2 ~ \text{where} ~b = 5.\\\\\\`

`\textbf{b)}\\\\~~~√(27) * √(75)\\\\=√(9 * 3) * √(25 * 3)\\\\=\sqrt 9 * \sqrt 3 * √(25) * \sqrt 3\\\\=3* 5 * \left(\sqrt 3 \right)^2\\\\=15 * 3\\\\=45`

Answer 2

a)b= 5

b)45

Explanation:

a) 5 times ten is 50 . the two factors of 50 are 25 and 2. The square root of 25 is 5, so that's the answer.

b) 27 × 75 is 2025 and the base root is 45², then with the radical and exponent we reduce the index by 2 to get 45.