Estimating Roots

Most roots are irrational — they never terminate or repeat as decimals:

• The square root of 2 is about 1.414
• The square root of 3 is about 1.732
• The square root of 5 is about 2.236

Estimate any root by finding the nearest perfect square. The square root of 50 falls between 7 and 8, closer to 7, since 49 is nearer than 64.

For cube roots, the same bracketing works. ∛100 is between ∛64 (4) and ∛125 (5), closer to 5 — roughly 4.64. This estimation skill is surprisingly useful in construction, engineering, and any field where you need to reverse an area or volume calculation quickly.