(√ 10 +3)(√ 10 - 3)
When I multiply the √ 10's what would it come out to be? That's what throws me off >_<
( a + b ) ( a - b ) = a ^ 2 - b ^ 2
[ sqrt ( 10 ) + 3 ] [ sqrt ( 10 ) - 3 ] =
sqrt ( 10 ) ^ 2 - 3 ^ 2 =
10 - 9 = 1
If your expression mean :
sqrt [ ( 10 ) + 3 ] sqrt [ ( 10 ) - 3 ]
then
sqrt [ ( 10 ) + 3 ] sqrt [ ( 10 ) - 3 ] =
sqrt ( 13 ) sqrt ( 7 ) =
sqrt ( 13 * 7 ) = sqrt ( 91 )
To multiply the expressions (√ 10 + 3) and (√ 10 - 3), we can use the "difference of squares" formula:
(a - b)(a + b) = a^2 - b^2
In this case, a = √10 and b = 3. So we have:
(√10 + 3)(√10 - 3) = (√10)^2 - 3^2
Now, let's simplify (√10)^2 and 3^2:
(√10)^2 = 10 (since the square of a square root cancels out)
3^2 = 9
Substituting these values back into the equation, we get:
(√10 + 3)(√10 - 3) = 10 - 9 = 1
Therefore, the product of (√10 + 3)(√10 - 3) is 1.