Divide 4√10 √2 provide an exact answer
To divide 4√10 by √2, we need to rationalize the denominator by multiplying both the numerator and the denominator by √2.
4√10 / √2 * √2/√2
Simplifying the expression gives:
(4√10 * √2) / (√2 * √2)
=(4√(10*2))/√(2*2)
=(4√20) / √4
= (4√20) / 2
= 2√20
Hence, the exact answer is 2√20.
To divide 4√10 by √2, we can simplify the expression as follows:
Step 1: Recall that √(a*b) = √a * √b. Therefore, we can rewrite 4√10 as 4 * √10.
Step 2: Now, divide 4 * √10 by √2:
(4 * √10) ÷ √2 = (4 / √2) * √10.
Step 3: Rationalize the denominator by multiplying both the numerator and denominator by √2:
(4 / √2) * (√10 * √2) = (4√2 / √2 * √2) * √10 = (4√2 / 2) * √10 = 2√2 * √10.
Step 4: Simplify the expression 2√2 * √10:
2√2 * √10 = 2 * √(2 * 10) = 2 * √20.
Step 5: Further simplify by factoring out the square root of a perfect square from within the radical:
2 * √(2 * 2 * 5) = 2 * √4 * √5 = 2 * 2 * √5 = 4√5.
Therefore, the exact answer to 4√10 ÷ √2 is 4√5.
To divide 4√10 by √2 and get an exact answer, we can simplify the expression by rationalizing the denominator.
Step 1: Recall that when we multiply the square root of a number by itself, we can eliminate the square root.
Step 2: Simplify 4√10 as follows:
4√10 = 4√(2*5) = 4√2√5 = 4(√2)(√5) = 4√2√5
Step 3: Simplify the denominator, √2, by multiplying it by the conjugate to rationalize it.
√2 * √2 = (√2)(√2) = √(2*2) = √4 = 2
Step 4: Divide 4√2√5 by √2:
(4√2√5)/√2 = (4/2)(√2√5) = 2(√2√5) = 2√10
The exact answer after dividing 4√10 by √2 is 2√10.