Find the Exponent of 2 in the Prime Factorisation of 144 Video Explanation Watch the video below for a clear explanation: Solution Question: The exponent of 2 in the prime factorisation of 144 is: (a) 4 (b) 5 (c) 6 (d) 3 Step 1: Prime Factorisation of 144 144 = 12 × […]
The exponent of 2 in the prime factorisation of 144, is (a) 4 (b) 5 (c) 6 (d) 3 Read More »
Prime Factors of the Denominator of a Rational Number with Decimal Expansion 327.7081 Video Explanation Watch the video below for the complete explanation: Solution Question: A rational number in its decimal expansion is 327.7081. What can you say about the prime factors of q when this number is expressed in the form p/q? Give reasons.
Prime Factorization of Denominators from Given Decimal Expansions Video Explanation Watch the video below for the complete explanation: Solution Question: What can you say about the prime factorizations of the denominators of the following rational numbers? Important Facts • A terminating decimal has denominator of the form 2m × 5n. • A non-terminating repeating decimal
Write the Denominator of 257/5000 in the Form 2m × 5n and Find Its Decimal Expansion Video Explanation Watch the video below for the complete explanation: Solution Question: Write the denominator of the rational number 257/5000 in the form 2m × 5n, where m and n are non-negative integers. Hence, write the decimal expansion without
Write the Decimal Expansions of the Given Rational Numbers Video Explanation Watch the video below for the complete explanation: Solution Question: Write down the decimal expansions of the following rational numbers by writing their denominators in the form of 2m × 5n, where m and n are non-negative integers. Important Rule If the denominator of
Terminating and Non-terminating Decimal Expansions Video Explanation Question Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion: (i) \( \frac{23}{8} \) (ii) \( \frac{125}{441} \) (iii) \( \frac{35}{50} \) (iv) \( \frac{77}{210} \) (v) \( \frac{129}{22 \times 5^7 \times 7^{17}}
Prove That √p + √q Is an Irrational Number Video Explanation Watch the video below for the complete explanation: Solution Statement: If p and q are prime positive integers, prove that √p + √q is an irrational number. Proof: Let us assume that √p + √q is a rational number. Then, squaring both sides, we
If p and q are prime positive integers, prove that √p + √q is an irrational number. Read More »
Prove That √p Is Irrational for Any Prime Positive Integer p Video Explanation Watch the video below for the complete explanation: Solution Statement: Prove that for any prime positive integer p, √p is an irrational number. Proof: Let us assume that √p is a rational number. Then we can write: √p = a / b
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Prove That 2 + 5√3 Is an Irrational Number Video Explanation Watch the video below for the complete explanation: Solution Question: Given that √3 is an irrational number, prove that 2 + 5√3 is an irrational number. Proof: Let us assume that 2 + 5√3 is a rational number. Since 2 is a rational number,
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Prove That (2 + √3)/5 Is an Irrational Number Video Explanation Watch the video below for the complete explanation: Solution Question: Given that √3 is irrational, prove that (2 + √3)/5 is an irrational number. Proof: Let us assume that (2 + √3)/5 is a rational number. Since 5 is a non-zero rational number, multiplying
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