√7
____
√10 - 3
2007-01-26 08:09:59 · 7 answers · asked by chris 2 in Science & Mathematics ➔ Mathematics
√7 √10 + 3
____ * ____ =
√10 - 3 √10 + 3
√70 + 3√7
___________ =
10-9
√70 + 3√7
2007-01-26 08:30:24 · answer #1 · answered by Bill F 6 · 0⤊ 1⤋
First: multiply the conjugate of the denominator with the numerator & denominator which is (â10 + 3)...
[(â7)(â10 + 3)] / [(â10 - 3)(â10 + 3)]
Sec: multiply the outer terms with the inner terms in parenthesis for the numerator & denominator...
[(â7)(â10)+(â7)(3)] / [â10)(â10)+(â10)(-3)+(3)(â10)+(3)(-3)]
[â70 + 3â7] / [â100 - 3â10 + 3â10 - 9]
[â70 + 3â7] / [â100 - 9]
[â70 + 3â7] / [10 - 9]
[â70 + 3â7] / 1
= â70 + 3â7
2007-01-27 01:02:34 · answer #2 · answered by ♪♥Annie♥♪ 6 · 0⤊ 0⤋
To rationalise the denominator you multiply both numerator (top half of fraction) and denominator (bottom half) by the denominator's conjugate. This will rationalise the denominator.
If the denominator is a+b, then the conjugate is a-b.
So the conjugate in this example would be sqrt(10)+3, and when you multiply through, the numerator is:
sqrt(7) x [sqrt(10)+3]
= sqrt(70) + 3 x sqrt(7)
The denominator becomes:
[sqrt(10) - 3] x [sqrt(10) + 3]
=[sqrt(10) x sqrt (10)] + [3 x sqrt(10)] - [3 x sqrt(10)] - [3 x 3]
= 10 - 9
= 1
2007-01-26 16:30:41 · answer #3 · answered by Raju M 1 · 0⤊ 0⤋
Multiply both numerator and denominator of your fraction by
sqrt(10) + 3.
Your new numerator will be sqrt(7)(sqrt(10) + 3)
Your new denominator will be 1
2007-01-26 16:21:58 · answer #4 · answered by MamaMia © 7 · 0⤊ 1⤋
multiply numerator and denomintor by the conjugate of the denominator (exploiting the difference of squares formula)
â7(â10 + 3)
_______________ =...
(â10 - 3)(â10 + 3)
2007-01-26 16:18:53 · answer #5 · answered by John D 3 · 0⤊ 0⤋
* root 10 + 3 over root 10 +3
2007-01-26 16:19:09 · answer #6 · answered by trier 2 · 0⤊ 1⤋
by multiplying the top and bottom by-3-sqrt(10):
2007-01-26 16:17:43 · answer #7 · answered by bruinfan 7 · 0⤊ 2⤋