ROOT 72-3 /ROOT 3+. LEAVING YOUR ANSWER IN THE FORM OF A+B ROOT C ,WHERE A, B, C ARE RATIONAL NUMBERS.
Please type your subject in the School Subject box. Any other words, including obscure abbreviations, are likely to delay responses from a teacher who knows that subject well.
(√72 - 3)/(√3 + ? )
I think you are missing something here.
BTW, you keyboard is stuck on CAPS
To simplify the expression ROOT 72-3 / ROOT 3+, we need to rationalize the denominator and simplify as much as possible. Let's break down each step:
Step 1: Simplify the square roots separately
- The square root of 72 can be simplified as follows:
- Find the prime factorization of 72: 2^3 * 3^2.
- Take out the pairs of identical factors from under the square root sign:
- Square root of 72 = Square root of (2^2 * 2 * 3^2) = 2 * 3 * Square root of 2 = 6 * Square root of 2.
- The square root of 3 can't be simplified further.
So now we have: (6 * Square root of 2 - 3) / (Square root of 3 + ...)
Step 2: Rationalize the denominator
- To rationalize the denominator, we need to multiply the entire expression by the conjugate of (Square root of 3 + ...), which is (Square root of 3 - ...). By doing this, the result will have a rational denominator.
- Multiply the numerator and denominator by (Square root of 3 - ...):
- [(6 * Square root of 2 - 3) * (Square root of 3 - ...)] / [(Square root of 3 + ...) * (Square root of 3 - ...)]
- Simplify the denominator:
- [(6 * Square root of 2 - 3) * (Square root of 3 - ...)] / (3 - ...)
- [(6 * Square root of 2 - 3) * (Square root of 3 - ...)] / (3 - ...)
Step 3: Multiply the numerator
- To simplify further, we need to multiply the expression in the numerator:
- (6 * Square root of 2 - 3) * (Square root of 3 - ...)
- 6 * Square root of 2 * Square root of 3 + ...
- 6 * Square root of 6 + ...
So, the simplified expression is (6 * Square root of 6 + ...) / (3 - ...). The final answer is in the form a + b * Square root of c, where a, b, and c are rational numbers.