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Unusual Long Division - Square Roots Before Calculators

Age 14 to 16
Challenge Level Yellow starYellow starYellow star
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The next digit of the answer is 5.

There are a number of ways of exploring around this area, don't rush.

You might try 'trial and improvement' as one way to work towards a square root of say 30, 50 or any other number.

Try this new method to find square roots for 30, 50, etc., then check with a calculator to see that it's working out correctly. Listen again to the audio as many times as you need. There's a lot of calculation to follow.

When you are ready, think about the harder questions:
  • Why multiply by 2 and by 10?

  • And why look for an end digit that is also the digit you use to multiply?


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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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