rationalize the denominator
7/(sqrt7)-(sqrt3)
What is being asked in the problem and what does that mean? What plan am I going to try? (1 sentence)
I will write out my response to the question, explaining my answer and what it means. (1 sentence)
also solve the problem
The problem is asking to simplify the expression by rationalizing the denominator, which means getting rid of square roots in the denominator. My plan is to multiply the numerator and denominator by the conjugate of the denominator to eliminate the radical in the denominator.
To rationalize the denominator in the expression 7/(sqrt7)-(sqrt3), we multiply the numerator and denominator by the conjugate of the denominator, which is sqrt7+sqrt3, resulting in (7(sqrt7+sqrt3))/(7-3). This simplifies to (7(sqrt7+sqrt3))/4.
I need the step by step solving of the equation
Sure! Here is the step-by-step solution:
1. Given expression: 7 / (√7 - √3)
2. Multiply the numerator and denominator by the conjugate of the denominator, which is (√7 + √3):
7 / (√7 - √3) * (√7 + √3) / (√7 + √3)
3. This gives: (7(√7 + √3)) / ((√7 - √3)(√7 + √3))
4. Expand the denominator using the difference of squares formula, (a - b)(a + b) = a^2 - b^2:
(7(√7 + √3)) / (7 - 3)
5. Simplify the denominator (7 - 3) to 4:
(7(√7 + √3)) / 4
6. Final simplified expression after rationalizing the denominator: (7(√7 + √3)) / 4
Therefore, the rationalized form of the expression is (7(√7 + √3)) / 4.