3 years ago

Which square root should be placed between the number 17 and 18 on the number line.

1 answer:

4 0

17^2 = 289
18^2 = 324
Any of the numbers between 289 and 324 exclusive will have a root between 17 and 18
Eg sr(300) = 17.3205... is between 17 and 18 on the number line.
There are 33 other whole number answers you could pick

You might be interested in

4. A football player forces at least 1 turnover in 27.5 percent of the games he plays. If the player plays in 57 games, in how m

Ostrovityanka [42]

The correct answer is 88

7 0

3 years ago

Prove that H c G is a normal subgroup if and only if every left coset is a right coset, i.e., aH = Ha for all a e G

Kaylis [27]

$\Rightarrow$

Suppose first that $H\subset G$ is a normal subgroup. Then by definition we must have for all $a\in H$ , $xax^{-1} \in H$ for every $x\in G$ . Let $a\in G$ and choose $(ab)\in aH$ ( $b\in H$ ). By hypothesis we have $aba^{-1} =abbb^{-1}a^{-1}=(ab)b(ab)^{-1} \in H$ , i.e. $aba^{-1}=c$ for some $c\in H$ , thus $ab=ca \in Ha$ . So we have $aH\subset Ha$ . You can prove $Ha\subset aH$ in the same way.

$\Leftarrow$

Suppose $aH=Ha$ for all $a\in G$ . Let $h\in H$ , we have to prove $aha^{-1} \in H$ for every $a\in G$ . So, let $a\in G$ . We have that $ha^{-1} =a^{-1}h'$ for some $h'\in H$ (by the hypothesis). hence we have $aha^{-1}=h' \in H$ . Because $a$ was chosen arbitrarily we have the desired .