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Squares and Square Roots

Squares and Square Roots · Class VIII

Slide n to see its square and slide N to see its square root.

7
type a value
030
144
type a value
01000
Live values
  • n^249
  • sqrt(N)12
  • Perfect square? (1 yes)1
xy
  • x^2

Formulas in this lab

  • n^2
    n2n^{2}
  • sqrt(N)
    N\sqrt{N}
  • Perfect square? (1 yes)
    [N∈Z][\sqrt{N} \in \mathbb{Z}]
Tip: The square root of N is the side of a square with area N.

Frequently asked questions

▶What is a square root?

The square root of N is the number which, when multiplied by itself, gives N. So sqrt(144) = 12 because 12 * 12 = 144. The lab takes any N up to 1000 and shows its square root, along with squares of n.

▶How do I use the squares and roots lab?

Slide n to see n^2 (the square) and slide N to see sqrt(N) (the square root). Try n = 7 to see 49, and N = 100 to see 10. The two sliders let you explore the link between squaring and taking the root.

▶How are squares used in Indian house plots?

A square plot of side 30 ft has area 30^2 = 900 sq ft. To check, if a plot has area 1600 sq ft and is square, its side is sqrt(1600) = 40 ft. The lab does both directions, useful for property and gardening calculations.

▶Perfect square vs non-perfect square: how to tell?

A perfect square has a whole-number root: 4, 9, 16, 25, 36 and so on. Non-perfect squares like 10 give 3.162..., a decimal that never ends cleanly. Slide N in the lab and watch the root flip between whole and decimal values.