Given that \(\sqrt{24025}=155\), then \(\sqrt{240.25}+\sqrt{2.4025}+\sqrt{0.024025}+\sqrt{0.00024025}\) is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 17.2205
Moving the decimal point two places in a number moves it one place in its square root, because \(\sqrt{100}=10\). Each number here is 24025 with the point moved 2, 4, 6 and 8 places to the left, so each root is 155 with the point moved 1, 2, 3 and 4 places:
\(\sqrt{240.25}=15.5\)
\(\sqrt{2.4025}=1.55\)
\(\sqrt{0.024025}=0.155\)
\(\sqrt{0.00024025}=0.0155\)
Sum: \(15.5+1.55+0.155+0.0155=17.2205\)
Tip: To take the square root of a decimal, the digits after the point must be in pairs; the root then has half as many decimal places (0.024025 has six, so its root has three).