Educational

Find the Number of Consecutive Zeros in n = 23 × 34 × 54 × 7 Video Explanation Watch the video below for a clear explanation: Solution Question: If n = 23 × 34 × 54 × 7 then the number of consecutive zeros in n, where n is a natural number, is: (a) 2 […]

Which Value Cannot Be the HCF When the LCM Is 1200? Video Explanation Watch the video below for a clear explanation: Solution Question: The LCM of two numbers is 1200. Which of the following cannot be their HCF? (a) 600    (b) 500    (c) 400    (d) 200 Important Property The HCF of two

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 ×

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

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