Question

В.чисельнику (корінь з 10 мінус корінь з 6).в.знаменнику (корінь з 15 мінус 3) Спростіть.вираз..будь-ласка!

Answer 1

Надеюсь понятно будет...

Answer 2

Simplifying the Expression

To simplify the given expression (the square root of 10 minus the square root of 6) divided by (the square root of 15 minus 3), we can follow these steps:

1. Rationalize the denominator to remove the radical from it. 2. Simplify the expression further if possible.

Let's proceed with the first step.

Rationalizing the Denominator

To rationalize the denominator, we can multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of the denominator is obtained by changing the sign between the terms.

The expression becomes:

((√10 - √6) / (√15 - 3)) * ((√15 + 3) / (√15 + 3))

Expanding this, we get:

((√10 - √6)(√15 + 3)) / ((√15 - 3)(√15 + 3))

Simplifying the Expression

Now, let's simplify the expression further.

The numerator can be expanded as follows:

√10 * √15 + √10 * 3 - √6 * √15 - √6 * 3

Simplifying this, we get:

√150 + 3√10 - √90 - 3√6

The denominator can be expanded as:

√15 * √15 + √15 * 3 - 3 * √15 - 3 * 3

Simplifying this, we get:

15 - 3√15 - 3√15 - 9

Combining like terms, we get:

√150 + 3√10 - √90 - 3√6 / 6 - 6√15 - 9

This is the simplified form of the given expression.

I hope this helps! If you have further questions or need additional assistance, feel free to ask.