(sqr8) {(sqr9ab)/(sqr3b) + (sqr27a)}
How do you solve this
just multiply roots like anything else. If a square root contains a perfect square, like 16 or 49, you can factor the 4 or 7 out of the root. For this problem,
√8(√(9ab)/√(3b) + √(27a))
2√2 (√(9ab/3b) + 3√(3a))
2√2 (√(3a) + 3√(3a))
2√2 * 4√(3a)
8√(6a)
Is that
√8( √(9ab)/√(3b) + √(27a) )
or
√8 { √(9ab)/ [√(3b) + √(27a) ] }
furthermore, is it (√9)(ab) or √(9ab) ?
same for the other square roots .
To solve this expression, we need to simplify it step by step:
1. Let's simplify each square root separately.
- The square root of 8 can be simplified as the square root of 4 multiplied by the square root of 2, which equals 2√2.
- The square root of 9 is simply 3.
- The square root of 3 can't be simplified further.
2. Now let's simplify the terms inside the brackets:
- (square root of 9ab) / (square root of 3b) can be simplified as follows:
The square root of 9ab is the square root of 9 multiplied by the square root of ab. Since the square root of 9 is 3, we have 3√(ab).
The square root of 3b can't be simplified further.
3. Simplifying the last term, the square root of 27a:
The square root of 27a can be simplified as the square root of 9 multiplied by the square root of 3a, which equals 3√(3a).
4. Now let's put it all together:
Substitute the simplified forms into the original expression:
2√2 + (3√(ab))/(√(3b)) + 3√(3a)
And that's the simplified form of the expression.