Question

1.√75/√3 и 2.√6^2 умножить на 3^4

Answer 1

1. To solve the expression √75/√3, we need to simplify each square root first.

The square root of 75 can be simplified by factoring it into its prime factors: 75 = 3 * 5 * 5.

Then, we can rewrite the square root of 75 as the square root of (3 * 5 * 5). Using the property of square roots, we can split the square root into two separate square roots: √(3 * 5 * 5) = √3 * √5 * √5.

Simplifying further, we have √3 * 5 * 5 = 5√3.

Next, let's simplify the square root of 3. Since 3 doesn't have any perfect square factors, we cannot simplify it any further. Therefore, the expression becomes (5√3) / √3.

To divide two square roots, we can multiply both the numerator and denominator by the conjugate of the denominator, which is √3.

(5√3 * √3) / (√3 * √3) = (5√3 * √3) / 3.

Multiplying the square roots, we have 5 * 3 = 15.

So, the simplified form of √75/√3 is 15.

2. Now let's solve the expression √6^2 * 3^4.

First, we evaluate √6^2. The square of 6 is 6 * 6 = 36. Therefore, √6^2 = √36 = 6.

Next, we evaluate 3^4. The fourth power of 3 is 3 * 3 * 3 * 3 = 81.

Now, we multiply the two results: 6 * 81 = 486.

So, the value of √6^2 * 3^4 is 486.

To summarize: 1. √75/√3 simplifies to 15. 2. √6^2 * 3^4 simplifies to 486.