Evaluating Steps in the Eleven Plus

Do you remember how to evaluate the square root of 405 768?

You will recall that you had to follow successive steps:

Mark off the digits from the right in groups of two

40 57 69

Look at the 40. Find the largest square number whose square is not greater than 40, i.e. 6

Put the 6 in the working above the 40.

Multiply 6 by 6, and subtract the result from 40, leaving 4.

Bring down the next group – the 57.

Double the 6 on the next line and put down 12 – to make the first part of the divisor.

124 times 4 is too big.

123 times 3 is 369.

Put 3 above the 57 – and also after the 12 to make 123.

Multiply 123 by 3 to obtain 369 and subtract this from the 457. This gives 88.

Double the 63 on the top line and put down 126 as the frst part of the divisor.

Put 7 on the top line and complete 1267 as the divisor.

Bring down the 69

You now have 88 69

Multiply the 1267 by 7 to find 8869

Take the 88 69 from the 88 69.

The square root of 405 768 is 637.

Prove this by multiply 637 by 637.

It may be an idea to work through this example yourself before trying it with your child.

Some eleven plus children, who know how to divide, will be able to follow these instructions. Some nine to ten year old children may find it a challenge.

Square roots of this nature are not, however, in the eleven plus!

Is long division really necessary in the eleven plus?