Consider the expression 36 −−−√

Question

x 53
. Will the product be rational or irrational? Explain how you know in one or two sentences, and then find the product. (2 points)

Answer 1

To evaluate the expression \( \sqrt{36} \times 53 \), we first simplify \( \sqrt{36} \), which equals 6. Thus, the expression simplifies to \( 6 \times 53 \).

Calculating that gives: \[ 6 \times 53 = 318. \]

Since both 6 and 53 are rational numbers, their product (318) is also a rational number. Therefore, the product is rational.