"question 3 Show how 5^(1/2) can be represented on the number line.
Class 9 - Math - Number Systems Page 8"
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Write a given number 5 without a square root at the sum of the square of two natural numbers then draw on number line and draw an Arc of radius √5 , take O as origin…
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Fig. is in the attachment
We have ,√5
Now 5 can be written as 5= 4+1= 2² + 1²
So we take OQ= 2 & PQ= 1
Now draw OQ= 2 units on the number line and then draw PQ= 1 unit, such that PQ _| OQ. join OP.
Now by Pythagoras Theorem we get
OP²= OQ²+PQ²
OP = √ OQ²+ PQ² =√2²+1²= √ 4+ 1= √5
On taking O as centre & OP = √5 as radius, draw an Arc which intersects the number line at point R.
Hence, the point R represents √5.
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______________________________________.
Fig. is in the attachment
We have ,√5
Now 5 can be written as 5= 4+1= 2² + 1²
So we take OQ= 2 & PQ= 1
Now draw OQ= 2 units on the number line and then draw PQ= 1 unit, such that PQ _| OQ. join OP.
Now by Pythagoras Theorem we get
OP²= OQ²+PQ²
OP = √ OQ²+ PQ² =√2²+1²= √ 4+ 1= √5
On taking O as centre & OP = √5 as radius, draw an Arc which intersects the number line at point R.
Hence, the point R represents √5.
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