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Hello everyone, welcome to R&H Academy channel. Today we will show exercise 1.2. Question number one is state whether the following statements are true or false, justify your answer. First part is, every irrational number is a real number. 
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We know that rational and irrational together form real numbers. Thus, every irrational number is a real number. Second part is, every point on the number line is of the form root m, where m is a natural number. It is false. 
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Since we can represent zero, or integers or fractions on the number line as well. The third part is every real number is an irrational number which is false. Because the real numbers also include rational numbers, so rational and irrational numbers together from real numbers. So rational numbers are also real numbers. 
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So every real number is not an irrational number. Question number two is, are the square root of all positive integers irrational? If not, give an example. Is under root four an irrational number? Four is a positive integer. And under root of four is equal to two, which is a natural number. Thus, the square root of all positive integers is not irrational. 
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Question number three says represent root five on the number line. For that we require the following. Follow the steps First step, draw a number line
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Step two, mark two centimeter on the number line
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Step three,
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mark it as A. So, OA is equal to two centimeter. Step number three, draw a perpendicular on A
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It should be equal to one centimeter.
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mark it as B.
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Join OB.
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Now OB is equal to root five.
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To represent root five on a number line, use a compass
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intersect the number line with O as center
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and radius equals to OB, mark it as C
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Now OC is equal to root five.
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Now,
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According to Pythagoras theorem.
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hypotenuse square is equal to base square plus perpendicular square. So hypotenuse is OB
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OB square
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is equal to perpendicular square AB
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square
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plus base square
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OA square
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AB is equal to one centimeter
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OA is equal to two centimeter.
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One square is one, two square is four, which is equivalent to five.
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So OB square is equal to five and OB is equal to root
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five. So you know how to represent root five on number line
