write the following square root in form a root b where a and b are intergers and b has the least value possible .
root 45=
√45 = √(9*5) = √9*√5 = 3√5
To rewrite the square root of 45 in the form of "a root b," where a and b are integers and b has the least value possible, follow these steps:
Step 1: Find the prime factorization of the number inside the square root (√45):
45 = 3 * 3 * 5
Step 2: Group pairs of the same prime factors and bring them outside the square root:
√45 = √(3 * 3 * 5)
Step 3: Simplify the square root expression:
√45 = √(3^2 * 5)
Step 4: Distribute the square root to each factor:
√45 = √(3^2) * √5
Step 5: Simplify the square root of the perfect square:
√45 = 3√5
So, the square root of 45 in the form of "a root b" is 3√5, where a = 3 and b = 5.