Given that #16 xx 36=576#, then find #sqrt(576)# without a calculator using properties of perfect squares?

1 Answer
Sep 23, 2017

Answer:

# sqrt(576) = 24 #

Explanation:

Given:

# 16 xx 36 = 576 #

Then we can manipulate the LHS, noting that both #16# and #36# are perfect squares to get:

# 16 xx 36 = 576 #

# :. 4 xx 4 xx 6 xx 6 = 576 #

# :. (4 xx 6) xx (4 xx 6) = 576 #

# :. (4 xx 6)^2 = 576 #

# :. (24)^2 = 576 #

Hence:

# sqrt(576) = 24 #