Suppose a and b are positive integers.
A) Verify that if a = 18 and b = 10, then √a * √b = 6√5.
B) Find two other pairs of positive integers a and b such that √a * √b = 6√5.
HELP!:(
A.
Well you just substitute a and b:
√a * √b
√18 * √10
To combine them, we just multiply the terms inside the radical sign and retain the radical sign:
√180
√(36*5)
√(6^2)(5)
6√5
B.
Well we know that 6√5 is also equivalent to √180. Therefore take a pair from the factors of 180. For example, from the first question, 10 and 18 are factor pair of 180 because 10 x 18 = 180.
Oookay, I see. Thank you so much, Jai!:D
To verify that √a * √b = 6√5 when a = 18 and b = 10, we can follow these steps:
1) Substitute the given values of a and b into the equation √a * √b and simplify:
√18 * √10 = √(18 * 10) = √180.
2) Simplify the square root of 180:
√(180) = √(36 * 5) = √36 * √5 = 6√5.
Therefore, we conclude that if a = 18 and b = 10, then √a * √b = 6√5.
To find two other pairs of positive integers a and b where √a * √b = 6√5, we have to follow these steps:
1) Rewrite the equation as √a * √b = 6√5.
2) We know that the square root of 5 cannot be simplified further, so we need to find two numbers whose square roots, when multiplied together, give us 6.
3) One such pair of numbers is 4 and 9, since √4 * √9 = 2 * 3 = 6. Therefore, a = 4 and b = 9.
4) Another pair can be 1 and 36, since √1 * √36 = 1 * 6 = 6. Therefore, a = 1 and b = 36.
Thus, two other pairs of positive integers a and b such that √a * √b = 6√5 are a = 4 and b = 9, and a = 1 and b = 36.