import{E as v,aj as N,r as a,s as Y,a as k,l as Q}from"./index-XCg2QAX4.js";import{b as m}from"./style-MaFG70fX.js";const y="Justify the existence of a square root",T=!0,E="mathLive",w="15/11/2023",O="55cc0",A="2N32-1";function L(){v.call(this),this.titre=y,this.nbQuestions=5,this.nbCols=2,this.nbColsCorr=2,this.sup=1,this.correctionDetaillee=!0,this.correctionDetailleeDisponible=!0,this.nouvelleVersion=function(){this.interactif?this.consigne="Does the proposed number exist? <br>Answer Yes or No.":this.consigne=" Does the proposed number exist? Justify.",this.listeQuestions=[],this.listeCorrections=[];const d=[1,2,3,4,5,6,7,8];let g;const D=N(d,this.nbQuestions);let c,u,o,p,l,n,q,b,i,f=0;for(let h=0,s,e,r,t,x=0;h<this.nbQuestions&&x<50;){g=D[h];const $=`${m("Definition")}: $\\sqrt{a}$ is the positive number whose square is $a$.<br>It therefore checks $\\sqrt{a}\\times \\sqrt{a}=a$. <br>As $a$ is a square, it is a positive number.<br>So, the square root of a negative number does not exist. <br><br>${m("Method")}: To show that a square root exists, simply show that the number under the radical is positive. <br><br>`;switch(g){case 1:c=a(2,9),t=`Since $\\sqrt{${c}} \\geqslant 0$, then $\\sqrt{\\sqrt{${c}}}$ exists. `,s=`$\\sqrt{\\sqrt{${c}}}$`,this.correctionDetaillee?(e=$,e+=t):e=t,r=["Yes","Yes","YES"];break;case 2:u=a(2,9)*-1,s=`$\\sqrt{${u}}$`,r=["No","No","NO"],t=`$${u}$ is a negative number so $\\sqrt{${u}}$ does not exist. `,this.correctionDetaillee?(e=$,e+=t):e=t;break;case 3:o=a(2,9)*-1,p=o*o,s=`$\\sqrt{\\left(${o}\\right)^{2}}$`,r=["Yes","Yes","YES"],t=`We have $\\left(${o}\\right)^{2}=\\left(${o}\\right)\\times \\left(${o}\\right)=${p}$. <br>As $${p}$ is a positive number, $\\sqrt{\\left(${o}\\right)^{2}}$ exists. `,this.correctionDetaillee?(e=$,e+=t):e=t;break;case 4:l=a(2,9),s=`$-\\sqrt{${l}}$`,r=["Yes","Yes","YES"],t=`${l} is a positive number so $-\\sqrt{${l}}$ exists.<br>${m("Noticed")}: The sign $-$ being placed in front of the radical symbol, the number $-\\sqrt{${l}}$ is therefore negative. `,this.correctionDetaillee?(e=$,e+=t):e=t;break;case 5:n=a(2,9)*-1,q=n*n,s=`$\\sqrt{-\\left(${n}\\right)^{2}}$`,r=["No","No","NO"],t=`We have $-\\left(${n}\\right)^{2}=-\\left(${n}\\right)\\times \\left(${n}\\right)=-${q}$.<br>Like $ -${q}$ is a negative number, $\\sqrt{-\\left(${n}\\right)^{2}}$ does not exist. `,this.correctionDetaillee?(e=$,e+=t):e=t;break;case 6:b=a(2,3),s=`$\\sqrt{${b}-\\pi}$`,r=["No","No","NO"],t=`Since $\\pi>3$ then $${b}-\\pi$ is a negative number. <br>Thus, $\\sqrt{${b}-\\pi}$ does not exist. `,this.correctionDetaillee?(e=$,e+=t):e=t;break;case 7:f=a(4,8),s=`$\\sqrt{${f}-\\pi}$`,r=["Yes","Yes","YES"],t=`Since $\\pi\\approx 3.14$ then $${f}-\\pi$ is a positive number.<br>Thus, $\\sqrt{${f}-\\pi}$ exists. `,this.correctionDetaillee?(e=$,e+=t):e=t;break;case 8:i=a(2,12),s=`$\\sqrt{-${i}^{2}}$`,r=["No","No","NO"],t=`We have $-${i}^{2}=-${i}\\times ${i}=-${i*i}$. <br>As $-${i*i}$ is a negative real, $\\sqrt{-${i}^{2}}$ does not exist. `,this.correctionDetaillee?(e=$,e+=t):e=t;break}Y(this,h,r,{formatInteractif:"text"}),this.interactif&&(s+=k(this,h,"largeur01 inline")),this.listeQuestions.indexOf(s)===-1&&(this.listeQuestions.push(s),this.listeCorrections.push(e),h++),x++}Q(this)}}export{w as dateDeModifImportante,L as default,T as interactifReady,E as interactifType,A as ref,y as titre,O as uuid};
//# sourceMappingURL=2N32-1-O2Jfh4XR.js.map