**Question 1. Prove that √5 is irrational.**

**Solution :**Let us assume, to the contrary, that √5 is rational.

That is, we can find integers a and b (≠ 0) such that :

a | ||

√5 | = | |

b |

So, b √5 = a⋅

CBSE Class 6th, 7th, 8th, 9th, & 10th | Help Guide | Solved Exercises | MCQs | Questions & Answers | Sample Papers

That is, we can find integers a and b (≠ 0) such that :

a | ||

√5 | = | |

b |

So, b √5 = a⋅

Labels:
CBSE Class X (10th) Mathematics,
coprime,
irrational number,
proof by contradiction,
rational number

(i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429

2 | | | 140 |

2 | | | 70 |

5 | | | 35 |

7 | | | 7 |

| | 1 |

∴ 140 = 2×2×5×7

= 2

- An algorithm is a series of well defined steps which gives a procedure for solving a type of problem. The word algorithm comes from the name of the 9th century Persian mathematician al-Khwarizmi.
- A lemma is a proven statement used for proving another statement.
**Euclid’s Division Lemma :**Given positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0 ≤ r < b.**Euclid’s division algorithm :**Euclid’s division algorithm is a technique to compute the Highest Common Factor (HCF) of two given positive integers. This is based on Euclid’s division lemma. According to this, the HCF of any two positive integers c and d, with c > d, is obtained as follows:

Labels:
al-Khwarizmi,
CBSE Class X (10th) Mathematics,
Composite Number,
Euclid’s division algorithm,
Highest Common Factor,
Prime Number,
Real Numbers,
The Fundamental Theorem of Arithmetic

This post contains links to solutions of all chapters for NCERT textbook of Science for Class 10th under CBSE.
Each link for the chapter provides solutions to questions given in its main exercises including multiple choice questions, numericals, activities and in-text questions given after a main section to check the under standing of the topic by students .

Which simply means that for our living,

Some substances are inert and cannot be acted upon by the microorganisms and do not breakdown into simple substances. Such substances are called non- biodegradable.

(a) a sunny day.

(b) a cloudy day.

(c) a hot day.

(d) a windy day.

(a) The field consists of straight lines perpendicular to the wire.

(b) The field consists of straight lines parallel to the wire.

(c) The field consists of radial lines originating from the wire.

(d) The field consists of concentric circles centred on the wire.

(a) 1/25

(b) 1/5

(c) 5

(d) 25

Each link, as given below, provides solutions to questions given in main exercises of the chapters, including multiple choice questions, numericals, activities and In Text questions given after a main section to check the under standing of the topic by students .

Subscribe to:
Posts (Atom)