Number
Squares and square roots
Square whole numbers and find the square roots of perfect squares.
Squaring a number means multiplying it by itself: 7² is 7 × 7 = 49. A number you get that way is called a perfect square. The square root runs the other way — √49 is 7, because 7 is the number that was squared. Every perfect square has a whole-number square root, and no other number does.
What the last digit tells you
A perfect square never ends in 2, 3, 7 or 8. It also never ends in an odd number of zeros. Those two facts alone rule out a great many numbers at a glance — 4832 cannot be a perfect square, and neither can 1000. And a square ending in 6 came from a number ending in 4 or 6, which narrows a search down fast.
Have a play
Every whole number from zero to twenty-five sits on this line. Find 1, 4, 9, 16 and 25 on it, and look at the gaps between them.
Tap anywhere on the line.
Worked example
Find √576 by prime factorisation.
Break 576 into primes: 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3.
Keep dividing by the smallest prime that goes in until only primes are left.
Try it together
Now let us find √1296 together.
Same method as the example: primes first, then pairs, then one number from each pair.
1.1296 breaks into 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3. How many complete pairs of the same prime can you make?
Have a go
Have a go on your own: 784 breaks into 2 × 2 × 2 × 2 × 7 × 7. What is √784?
Hint: One number from each pair, multiplied together.
Ready to practise?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.